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Ah, remember the days when you just got numbers to work out? Those earlier days were to help you to prepare for these days and beyond because life and math isn’t always so straightforward. It takes some thinking. It takes some maneuvering of facts and figures in order to find a solution to the mathematical problem. Some problems will be rather easy to work through while others - well, they are just brain teasers.

1.

Sir Patrick and his page Jake could travel 12 miles in 1 day. They were traveling from Gaul heading back to Rome, which is 600 miles away. A big flood flooded their path so they had to wait 4 days for conditions to improve before they could continue. A band of outlaws attacked them and stopped their travels for another 2 days. How many days did it take them in all to get from Gaul to Rome?

46

56

36

66

2.

Darren has *x* video games that if multiplied by 275 then multiplied by .30 that is then divided by 5 equals 3,564. How many video games does Darren have?

196

228

216

184

Working the problem:

To find the answer you need to work backwards, changing your math calculations as follows:

Start with multiplying 3,564 by 5

3,564 x 5 = 17,820

17,820 is then divided by .30

17,829 ÷ .30 = 59,400

59,400 is then divided by 275

59,400 ÷ 275 = 216

Test it out now

216 x 275 = 59,400

59,400 x .30 = 17,820

17,820 ÷ 5 = 3,564 - It works out!

__Solution__: Darren has 216 video games

Answer (c) is the correct answer

To find the answer you need to work backwards, changing your math calculations as follows:

Start with multiplying 3,564 by 5

3,564 x 5 = 17,820

17,820 is then divided by .30

17,829 ÷ .30 = 59,400

59,400 is then divided by 275

59,400 ÷ 275 = 216

Test it out now

216 x 275 = 59,400

59,400 x .30 = 17,820

17,820 ÷ 5 = 3,564 - It works out!

Answer (c) is the correct answer

3.

Four boys work together painting houses for the summer. For each house they paint they get $256.00. If the boys work for 4 months of the summer and their expenses are $152.00 per month, how many houses must they paint for each of them to have one thousand dollars at the end of the summer?

25

11

18

14

Working the problem:

152 x 4 (months) = 608 (for total expenses)

1000 x 4 (boys) = 4000

4000 + 608 = $4,608.00

The boys will need to make $4,608.00

4,608 ÷ 256 (per house) = 18

__Solution__: The boys will need to paint 18 houses

Answer (c) is the correct answer

152 x 4 (months) = 608 (for total expenses)

1000 x 4 (boys) = 4000

4000 + 608 = $4,608.00

The boys will need to make $4,608.00

4,608 ÷ 256 (per house) = 18

Answer (c) is the correct answer

4.

Sir Cameron and Sir Connor cleaned the rust off of helmets by rolling them in the sand. Cameron could clean 13 helmets in one day, and Connor could clean 10 helmets in one day. After 7 days, how many more helmets would Cameron have cleaned?

21

19

17

23

Working the problem:

Cameron: 13 helmets x 7 = 91 helmets in 1 week

Connor: 10 helmets x 7 = 70 helmets in 1 week

91 - 70 = 21

__Solution__: Cameron cleaned 21 more helmets

Answer (a) is the correct answer

Cameron: 13 helmets x 7 = 91 helmets in 1 week

Connor: 10 helmets x 7 = 70 helmets in 1 week

91 - 70 = 21

Answer (a) is the correct answer

5.

Suzy is ten years older than Billy, and next year she will be twice as old as Billy. How old are they now?

Billy is 4 and Suzy is 14

Billy is 19 and Suzy is 29

Billy is 8 and Suzy is 18

Billy is 9 and Suzy is 19

Working the problem:

Billy age 10 x 2 = 20 (Suzy)

10 - 1 = 9 ........ 20 - 1 = 19

__Solution__: Billy is 9 and Suzy is 19

Answer (d) is the correct answer

Billy age 10 x 2 = 20 (Suzy)

10 - 1 = 9 ........ 20 - 1 = 19

Answer (d) is the correct answer

6.

Arthur wants to take his wife to Hawaii for five days. He estimated that the trip will cost him $3,600. He has $1,000 in the bank that he can use but must save up another $2,600 in 8 weeks. How much will he have to save each week to save up the remaining $2,600?

$265.00

$325.00

$295.00

$315.00

Working the problem:

$3,600.00 - $1,000.00 = $2,600.00

$2,600.00 ÷ 8 = $325.00

__Solution__: Arthur must save $325.00 each week

Answer (b) is the correct answer

$3,600.00 - $1,000.00 = $2,600.00

$2,600.00 ÷ 8 = $325.00

Answer (b) is the correct answer

7.

The Weber Zoo has a total of 316 animals. Of those, 211 are large animals and 105 are smaller animals. It costs the zoo $14 per day to feed each of the larger animals and $9 per day to feed each of the smaller animals. How much does it cost the zoo each month (30 days) to feed all of the animals?

$116,970.00

$16,970.00

$161,790.00

$611,970.00

Working the problem:

211 (large animals) x 14 = 2,954 per day

105 (smaller animals) x 9 = 945 per day

2,954 + 945 = 3,899

$3,899 per day x 30 = $116,970.00

__Solution__: It costs the zoo $116,970.00 each month to feed all of the animals

Answer (a) is the correct answer

211 (large animals) x 14 = 2,954 per day

105 (smaller animals) x 9 = 945 per day

2,954 + 945 = 3,899

$3,899 per day x 30 = $116,970.00

Answer (a) is the correct answer

8.

Trip to the Lake Question:

The Deweys' car gets 20 miles per gallon (mpg)

The Stones' car gets 30 miles per gallon (mpg)

The Webers' car gets 15 miles per gallon (mpg)

The Golds' car gets 24 miles per gallon (mpg)

Four families traveled from different places to vacation together at a lake.

The Deweys drove 210 miles

The Webers drove 50 miles less than the Deweys drove

The Golds drove 100 miles more than the Webers drove

The Stones drove 110 miles more than the Webers drove

How many gallons of gas did each family use to get to the lake?

(Round answers to the nearest tenth)

The Deweys' car gets 20 miles per gallon (mpg)

The Stones' car gets 30 miles per gallon (mpg)

The Webers' car gets 15 miles per gallon (mpg)

The Golds' car gets 24 miles per gallon (mpg)

Four families traveled from different places to vacation together at a lake.

The Deweys drove 210 miles

The Webers drove 50 miles less than the Deweys drove

The Golds drove 100 miles more than the Webers drove

The Stones drove 110 miles more than the Webers drove

How many gallons of gas did each family use to get to the lake?

(Round answers to the nearest tenth)

Deweys used 11.5 gallons of gas; Webers used 12.5 gallons of gas; Golds used 10.9 gallons of gas; and Stones used 8 gallons of gas

Deweys used 10.5 gallons of gas; Webers used 10.7 gallons of gas; Golds used 10.8 gallons of gas; and Stones used 9 gallons of gas

Deweys used 10.5 gallons of gas; Webers used 11.6 gallons of gas; Golds used 11.8 gallons of gas; and Stones used 7 gallons of gas

Deweys used 12 gallons of gas; Webers used 13.7 gallons of gas; Golds used 12.8 gallons of gas; and Stones used 13 gallons of gas

Working the problem:

Deweys drove 210 miles

Webers drove 210 - 50 miles = 160 miles

Golds drove 160 + 100 = 260 miles

Stones drove 160 + 110 = 270 miles

Deweys -- 210 miles divided by 20 (mpg) = 10.5 gallons

Webers -- 160 miles divided by 15 (mpg) = 10.7 gallons

Golds -- 260 miles divided by 24 (mpg) = 10.8 gallons

Stones -- 270 miles divided by 30 (mpg) = 9 gallons

__Solution__: Deweys used 10.5 gallons of gas; Webers used 10.7 gallons of gas; Golds used 10.8 gallons of gas; and Stones used 9 gallons of gas

Answer (b) is the correct answer

Deweys drove 210 miles

Webers drove 210 - 50 miles = 160 miles

Golds drove 160 + 100 = 260 miles

Stones drove 160 + 110 = 270 miles

Deweys -- 210 miles divided by 20 (mpg) = 10.5 gallons

Webers -- 160 miles divided by 15 (mpg) = 10.7 gallons

Golds -- 260 miles divided by 24 (mpg) = 10.8 gallons

Stones -- 270 miles divided by 30 (mpg) = 9 gallons

Answer (b) is the correct answer

9.

The Smith family has four children (Jr., Buddy, Zach and Clarissa) who will be going to four different summer camps for two weeks. It is costing the Smith’s $835 in total to send all four children. It is costing twice as much to send Jr. to camp as it is costing to send Clarissa to camp. Buddy’s cost is $25 more than Clarissa’s and Zach’s cost is $170 which is $150 less than Jr.’s cost. How much is it costing to send each child?

Jr.’s cost is $320.00; Buddy’s cost is $175.00; Zach’s cost is $180.00; and Clarissa’s cost is $160.00

Jr.’s cost is $160.00; Buddy’s cost is $185.00; Zach’s cost is $170.00; and Clarissa’s cost is $320.00

Jr.’s cost is $290.00; Buddy’s cost is $195.00; Zach’s cost is $140.00; and Clarissa’s cost is $145.00

Jr.’s cost is $320.00; Buddy’s cost is $185.00; Zach’s cost is $170.00; and Clarissa’s cost is $160.00

Working the problem:

Total cost for all four children is $835.00

Zach’s cost is $170.00

$170.00 + $150.00 = $320.00 which is Jr.’s cost

$320.00 ÷ 2 = $160.00 which is Clarissa’s cost

$160.00 + $25.00 = $185.00 which is Buddy’s cost

__Solution__: Jr.’s cost is $320.00; Buddy’s cost is $185.00; Zach’s cost is $170.00; and Clarissa’s cost is $160.00

320 + 185 = 170 + 160 = 835

Answer (d) is the correct answer

Total cost for all four children is $835.00

Zach’s cost is $170.00

$170.00 + $150.00 = $320.00 which is Jr.’s cost

$320.00 ÷ 2 = $160.00 which is Clarissa’s cost

$160.00 + $25.00 = $185.00 which is Buddy’s cost

320 + 185 = 170 + 160 = 835

Answer (d) is the correct answer

10.

Jack walked from Santa Clara to Palo Alto. It took 1 hour 25 minutes to walk from Santa Clara to Los Altos. Then it took 25 minutes to walk from Los Altos to Palo Alto. He arrived in Palo Alto at 2:45 P.M. At what time did he leave Santa Clara?

11:55 AM

12:45 PM

12:55 PM

12:15 PM

Working the problem:

2:45 PM minus 25 minutes = 2:20 PM (he was in Los Altos)

2:20 PM minus 1 hr. and 25 minutes = 1:20 - 25 minutes = 12:55 PM

__Solution__: Jack left Santa Clara at 12:55 PM

Answer (c) is the correct answer

2:45 PM minus 25 minutes = 2:20 PM (he was in Los Altos)

2:20 PM minus 1 hr. and 25 minutes = 1:20 - 25 minutes = 12:55 PM

Answer (c) is the correct answer

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600 (miles) divided by 12 (miles) = 50 days

50 days + 4 (days layover) = 54 days

54 days + 2 (additional delays) = 56

It will take them 56 days to reach RomeSolution:Answer (b) is the correct answer