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Question:

Kevin and Kara are in a pancake-eating contest. Kevin can eat three pancakes per minute, while Kara can eat \(3\frac{\mathrm{1} }{\mathrm{2} }\) pancakes per minute. How many total pancakes can they eat in 10 minutes?

A 65 pancakes

explanation

If Kevin eats 3 pancakes in one minute, you know he eats 3(10) = 30 in 10 minutes. If Kara eats \(3\frac{\mathrm{1} }{\mathrm{2} }\) per minute, she eats 3.5 × 10 = 35 in 10 minutes. Add 30 + 35 = 65 and you have your answer.

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\(\frac{\mathrm{b+c} }{\mathrm{a} } = \frac{\mathrm{b} }{\mathrm{a} } + \frac{\mathrm{c} }{\mathrm{a} } \) defines which of the following?

distributive property for division

The distributive property for division helps in solving expressions like \(\frac{\mathrm{b+c} }{\mathrm{a} }\) . It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \(\frac{\mathrm{b+c} }{\mathrm{a} } = \frac{\mathrm{b} }{\mathrm{a} } + \frac{\mathrm{c} }{\mathrm{a} }\) . For example, \(\frac{\mathrm{ a^3+6 a^2 } }{\mathrm{ a^2 } } = \frac{\mathrm{ a^3 } }{\mathrm{ a^2 } } + \frac{\mathrm{6 a^2 } }{\mathrm{ a^2 } } = a+6\).

At a used book store, Valentina purchased three books for $2.65 each. If she paid with a $20 bill, how much change did she receive?

$12.05

Three books at $2.65 would equal a total of $7.95. The change would equal $20 − $7.95 = $12.05.

Which of the following is a prime number?

2

A prime number is a whole number that can be divided evenly by itself and by 1 but not by any other number. 2 is a prime number because its only factors are 1 and 2. 27 has factors of 1, 3, 9, and 27; 9 has factors of 1, 3, and 9; and 12 has factors of 1, 2, 3, 4, 6, and 12.

If each book's weight is \(\frac{\mathrm{1} }{\mathrm{3} }\) pounds, how many paperback books together weigh 25 pounds?

75

If each book weighs \( \frac{\mathrm{1} }{\mathrm{3} }\) pound, then 1 pound = 3 books. To find the number of books in 25 pounds, simply multiply this 3 by 25: 25×3=75.

Ellie wants to give her granddaughter a present of $500 saved in a bank account. If Ellie puts $350 in the account which earns an 8% annual interest rate, how long must she wait before the account is worth $500?

5 years 4 months

The interest amount is $150, which is the difference between the desired amount and what Ellie originally deposits. You can use the interest formula: I = Prt, where I interest, P is principal, r is rate, and t is time. Just plug in I = 150, P = 350, and r = 0.08, and solve for t: 150 = 350(0.08)t =28t = 150t ÷ 28 = 5.36 years, or approximately 5 years 4 months.

A baker uses 6 eggs to bake a cake. How many cakes will he be able to bake with 145 eggs?

24

To find out how many cakes the baker will be able to make, divide the total number of eggs (145) by the number needed to make a single cake (6): 145 ÷ 6 = 24

A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 50% off." If Frank buys two shirts, each with a regular price of $49, how much money will he save?

$24.50

By buying two shirts, Frank will save \(49 \times \frac{\mathrm{50} }{\mathrm{100}} = 24.5\).

What is the result when 7 is added to the product of 2 and 3?

13

To get your desired answer of 2(3) + 7 = 13 you will need to find out which mathematical operation you should perform first. Use the acronym PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) to determine the order of operations. In this problem, perform the multiplication operation first, followed by addition.

A florist has 733 flowers. How many full bouquets of 16 flowers can he make?

45

To find this value, it is simply necessary to divide the total number of flowers (733) by the number of flowers that will be in each bouquet (16): 733 ÷ 16 = 45.8
He will be able to make 45 full bouquets. He doesn’t have enough to complete the 46th one.

A Mayor won an election with 53% of the popular vote. The town's population is 26,000 and 85% of the town's people voted. How many votes did the Mayor receive to win?

11,713

If 85% of the town's 26,000 voters cast ballots the number of votes cast is: \( \frac{\mathrm{85} }{\mathrm{100}} \times 26000 = 0.85 \times 26000 = 22100\) The mayor got 53% of the votes cast which is: \(\frac{\mathrm{53} }{\mathrm{100} } \times 22100 = 0.53 \times 22100 = 11713\)

What is twelve percent as a fraction?

\( \frac{\mathrm{3} }{\mathrm{25} } \)

To change a fraction into a percent, divide by 100.
12% = \(\frac{\mathrm{12} }{\mathrm{100} } = \frac{\mathrm{3} }{\mathrm{25} } \)

A grocery manager sells 2 bags of potatoes for each bag of carrots. He also sells 6 bags of onions for each bag of potatoes. If he sells 12 bags of onions, how many bags of carrots will he sell?

1

First, figure out how many bags of potatoes would be sold if six bags of onions were sold. The ratio of onions sold to potatoes sold is 6: 1. So, if he sells 12 bags of onions, we must divide this number by six to get the number of bags of potatoes sold: 12 ÷ 6 = 2
Then, use this number to figure out how many bags of carrots he would sell:
The problem tells us that he sells two bags of potatoes for each bag of carrots. Therefore, he would sell 1 bag of carrots if he sold 12 bags of onions.

The total water usage for a city is 35,000 gallons each day. Of that total, 31% is for personal use and 49% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?

6,300

49% of the water consumption is industrial use and 31% is personal use so (49% - 31%) = 18% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes 18/100 x 35,000 gallons = 6,300 gallons.