2009 Grade 8 CEMC Gauss Problems/Problem 17

Problem

A jar contains quarters (worth $$0.25$ each), nickels (worth $$0.05$ each), and pennies (worth $$0.01$ each). The value of the quarters is $$10.00$ . The value of the nickels is $$10.00$ . The value of the pennies is $$10.00$ . If Judith randomly chooses one coin from the jar, what is the probability that it is a quarter?

$\text{ (A) }\ \frac{25}{31} \qquad\text{ (B) }\ \frac{1}{31} \qquad\text{ (C) }\ \frac{1}{3} \qquad\text{ (D) }\ \frac{5}{248} \qquad\text{ (E) }\ \frac{1}{30}$

Solution

Using the total value of the coins divided by how much each coin is worth, we can find out how many quarters, nickels, and pennies there are. This would allow us to find the probability of picking a quarter by dividing the number of quarters by the total number of coins.

There are $\frac{10.00}{0.25} = \frac{10.00 \times 4}{0.25 \times 4} = \frac{40.00}{1} = 40$ quarters.

There are $\frac{10.00}{0.05} = \frac{10.00 \times 20}{0.05 \times 20} = \frac{200.00}{1} = 200$ nickels.

There are $\frac{10.00}{0.01} = \frac{10.00 \times 100}{0.01 \times 100} = \frac{1000.00}{1} = 1000$ pennies.

This means there are $40 + 200 + 1000 = 1240$ coins altogether.

Dividing the number of quarters by the total number of coins, we get:

$\frac{40}{1240} = \frac{1}{31}$

~anabel.disher

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2009 Grade 8 CEMC Gauss Problems/Problem 17

Problem

Solution