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Question:

Karen is 6 years older than her sister Michelle, and Michelle is 2 years younger than their brother David. If the sum of their ages is 62, how old is Michelle?

A 18

explanation

Let: x = Michelle's age
x + 6 = Karen's age
x + 2 = David's age
State the problem in an equation:
x + x + 6 + x + 2 = 62
3x + 8 = 62
3x + 8 - 8 = 62 - 8
3x = 54
3x ÷ 3 = 54 ÷ 3
x = 18
This is Michelle's age.

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Standing by a pole, a boy 3(1/2)feet tall casts a 6-foot shadow. The pole casts a 24-foot shadow. How tall is the pole?

14 feet

Using the ratio height/shadow, the proportion 3(1/2)/6 = x/24 models this situation, where x represents the height of the pole. Cross multiply. 3(1/2)*24 =6x, so 84 = 6x, and x = 84/6 = 14 feet.

Yan can read two pages in 3 minutes. At this rate, how long will it take him to read a 360-page book?

9 hours

Using the ratio pages/minutes, the proportion 2/3 = 360/x can be used to find the time. Cross multiply. 2x = 3 × 360, so 2x = 1,080 and x =1080/2 = 540 minutes. Convert minutes to hours. There are 60 minutes in 1 hour so 540/60 = 9 hours.

Terry earns three times more per hour than Tim. Tim earns $2 more per hour than Angie. As a group they earn $43 per hour. What’s Angie’s hourly wage?

$7.00

Let x equal Angie’s hourly wage. x + 2 would then represent Tim’s hourly wage, and 3(x + 2) would represent Terry’s hourly wage.
x + (x +2) + 3(x +2) = 43
x + x + 2 + 3x + 6 = 43
5x + 8 = 43
5x = 35
x = 35/5
x = 7

Theodore has 20 baseball cards. He sells 1/4 of his cards to Tom, 1/3 of his cards to Larry, and his Mom accidently throws away 1/6 of his cards. How many baseball cards does Theodore have left?

5

Convert the different denominators to a common denominator that all the denominators can divide into evenly. 4, 3, and 6 all divide evenly into 12. To convert 1/4 to x/12, divide 12 (the new common denominator) by 4 (the old common denominator) to get 3. Then multiply 1/4 by 3/3 (another way of saying 1). The product is 3/12. (1/4 = 3/12). Do the same calculation for the other fractions: 1/3 = 4/12 and 1/6 = 2/12. Then add the new numerators together: 3 + 4 + 2 = 9. This gives you your new added numerator. Place the added numerator over the new denominator, and you can see that 9/12 of the cards have been sold or lost. 9/12 can be reduced to 3/4. 3/4 or 75% of the cards have been sold or lost. 20 × 0.75 = 15. 15 of 20 cards have been sold or lost. 20 – 15 = 5 cards remaining.

The product of two consecutive odd numbers is 399. What are the numbers?

19 and 21

The fastest way to solve this would be to simply multiply the possible choices together (19 × 21 = 399). You can also solve this with algebra. Let x equal the first number and x + 2 the second number.
x(x + 2) = 399
x² + 2x = 399 (Note: This is a quadratic equation that can be solved by setting it equal to zero and factoring.)
x² + 2x – 399 = 0
(x – 19)(x + 21) = 0
x – 19 = 0 OR x + 21 = 0
x = 19 OR x = –21
x + 2 = 21 OR x + 2 = –19
Two solutions are possible: 19 and 21, and –21 and –19. Because the latter pair isn’t one of the answer choices, the first pair is the correct answer.

Two go-carts are racing on a circular track with a perimeter of 360 feet. Camera One is following Go-Cart One, and Camera Two is following Go-Cart Two. If the angle between the two cameras is 40 degrees, how far apart are the two go-carts?

40 feet

A circle is 360 degrees, so 40 degrees is 1/9 of a circle (360 ÷ 40 = 9). To get the answer of 40 feet, multiply the perimeter of the track 1/9 (360 × 1/9 = 40).

Roxanne deposited $300 into a savings account earning 5(1/4)% annually. What is her balance after 1 year?

$315.75

Interest earned in 1 year is $300 * 5(1/4)% =$15.75. The total amount of the account after 1 year is $300 + $15.75 = $315.75.

Your piggy bank contains $19.75 in dimes and quarters. There are 100 coins in all. How many dimes are there?

35

Let x equal the number of dimes. Then 100 – x represents the number of quarters. There is $0.10x in dimes and $0.25(100 – x) in quarters.
0.10x + 0.25(100 – x) = 19.75
0.10x + 25 – 0.25x = 19.75
–0.15x = –5.25
x = –5.25/–0.15
x = 35

The length of a rectangle is three times its width. If the perimeter of the rectangle is 48, what is its area?

108

The perimeter of a rectangle is l + w + l + w = 48. Since l = 3w, the perimeter is 3w + w + 3w + w = 48 so 8w = 48 and w = 6. Therefore, the length is 3 × 6 or 18 and the area of the rectangle is l × w = 18 × 6 = 108.

Tiling costs $2.89 per square foot. What is the cost to tile a kitchen whose dimensions are 4 yards by 5 yards?

$520.20

There are 3 feet in a yard, so a kitchen 4 yards by 5 yards is equivalent to (4 × 3) feet by (5 × 3) feet, or 12 feet by 15 feet. The area of the kitchen is 12 × 15 = 180 square feet. The cost to tile is $2.89 × 180 = $520.20.

The cost of a protein bar increased from $2.50 to $2.80. The percent increase to the $2.80 rate was how much?

12%

First subtract the old cost from the new cost: $2.80 – $2.50 = $0.30. Then divide the difference by the old cost to find the percent difference: $0.30 ÷ $2.50 = 0.12 = 12%.

Theresa bought 5 karaoke CDs on sale. A karaoke CD normally costs $24, but she was able to purchase the CDs for $22.50 each. How much money did Theresa save on her entire purchase?

$7.50

Subtract the sale price from the regular price: $24.00 – $22.50 = $1.50. Multiply the remainder by the number of CDs to get your answer: $1.50 × 5 = $7.50.

The sun is 93 million miles from Earth and light travels at a rate of 186,000 miles per second. How long does it take for light from the sun to reach the Earth?

8.5 minutes

The distance formula is distance equals rate times time, or d = rt. Substituting the known values results in 93,000,000 = 186,000*t. So, t = 500 seconds. Divide 500 by 60 to convert to minutes (8 and 1/2 minutes).

What is the cost of putting grass seed on a 480-square-yard field, if a bag of grass seed covers 60 square yards and costs $7.45?

$59.60

Since 480 ÷ 60 = 8, you need 8 bags to cover the yard. Since each bag costs $7.45, the total cost will be $7.45 × 8 = $59.60.

What is the estimated product when 620 and 374 are rounded to the nearest hundred and multiplied?

240,000

620 is rounded to 600; 374 is rounded to 400. 600 * 400 = 240,000.