Question 1

Every U.S. dollar spent on foreign aid buys five gallons of clean water to distribute to people in need. Out of every five gallons of clean water intended for people in need, two gallons are lost due to environmental factors, transportation problems and conflict. If the United States spends $12 million on foreign aid in one year, how much of that money would actually make it to the people in need if spent on water?

Accepted Answer

If the United States spends $12 million on foreign aid in a year and three-fifths of the aid does not make it to the people in need, only $7.2 million dollars reaches the intended destination. Since two of the five gallons of water are lost, only three-fifths (or 60 percent) of it is successfully delivered. Sixty percent of $12 million dollars (12,000,000 x 0.6) is $7.2 million dollars.

Question 2

In a game, one card is drawn from a complete deck of playing cards without jokers. If the card is a club or a queen, the gambler wins double his bet. Otherwise, the dealer keeps the money. How much better are the dealer's odds in this game?

Accepted Answer

In a game where the dealer keeps a gambler's wager if he draws any card but a club or queen, his odds are 38% better than the gambler's of winning the money. There are 52 cards in a deck and 13 cards in each suit, including clubs. There are four queens in each deck, but the queen of clubs has already been counted, so only the queens of hearts, diamonds and spades count toward the gambler's list of winning cards. Therefore, the gambler needs one of 16 cards to be pulled in order to win, which make his odds of winning 31%. If his odds are 31%, the gambler's odds are the far superior 69%, which is better by 38%.

Question 3

If Martin invests $20,000 for 20 years and his investment earns 20% interest compounding quarterly, what will it be worth at the end of his investment period?

Accepted Answer

A $20,000 investment that earns 20% interest compounded quarterly would be worth $991,228.82 at the end of a 20-year investment period. The equation for compound interest is A = P(1 + r/n)nt in which A is the amount including interest, P is the principle investment, r is the interest rate expressed in decimal form (0.12), n is the number of times interest is added per year, and t is the number of years for which the principal is invested. A = $20,000(1+.2/4)80. = $991,228.82.

Question 4

To find the percentage (p) of any number (n), which formula can be used?

Accepted Answer

To find the percentage of any number, such as 42% of 677, for example, multiply the percentage in its whole value by the number, then divide the product by 100. (42 x 677) ÷ 100 = 284.34.

Question 5

If two cities are 500 miles apart, approximately how many kilometers apart are they?

Accepted Answer

A distance of 500 miles is approximately 805 kilometers long. Miles are longer than kilometers, so the value must be higher than 500. Therefore, 295 kilometers and 375 kilometers can be ruled out right away.

Question 6

If 11,300 people apply for entrance to an institution for which there is an 11% acceptance rate, how many people are offered admission?

Accepted Answer

11% of 11,300 is 1,243. Percentages are decimal fractions and must be put into those terms to use in an equation (11% = 0.11). Multiply the percentage by the whole group (0.11 x 11,300 = 1,243).

Question 7

If Jack invests $2,500 for one year and his investment is worth $2,825 at the end of that period, how much interest did he earn on his investment?

Accepted Answer

If Jack invested $2,500 and had $2,825 at the end of his investment period, he earned 13% interest during the year. The equation for simple interest in one term is V = P(1 + i) in which V represents the value with interest added, P is the principle investment and i is the amount of interest accrued during the term. To solve for the interest, divide V by P ($2,825 ÷ $2,500), then subtract 1. The difference (0.13) is the interest rate.

Question 8

If Elizabeth invests $4,000 for five years and her investment earns 12% interest, compounding annually, what will it be worth at the end of her investment period?

Accepted Answer

A $4,000 investment that earns 12% interest compounded annually would be worth $7,049.37 at the end of a five-year investment period. The equation for compound interest is A = P(1 + r/n)nt in which A is the amount including interest, P is the principle investment, r is the interest rate expressed in decimal form (0.12), n is the number of times interest is added per year, and t is the number of years for which the principal is invested. A = $4000(1+.12/1)5. = $7,049.37.

Quiz 23: Mathematics