2006 CEMC Pascal Problems/Problem 6

Problem

Ravindra and Hongshu made a pizza together. Ravindra ate $\frac{2}{5}$ of the pizza. Hongshu ate half as much as Ravindra. What percentage of the original pizza was left?

$\text{ (A) }\ 20 \qquad\text{ (B) }\ 30 \qquad\text{ (C) }\ 40 \qquad\text{ (D) }\ 50 \qquad\text{ (E) }\ 60$

Solution 1

Using the numbers given in the problem, we can see that Hongshu ate $\frac{2}{5} \div 2 = \frac{1}{5}$ of the pizza.

Summing the fractions to see how much pizza they ate, we can see that they ate $\frac{2}{5} + \frac{1}{5} = \frac{2 + 1}{5} = \frac{3}{5}$ of the pizza.

We now need to subtract this from the whole pizza to see how much pizza is remaining. We can then see that $\frac{5}{5} - \frac{3}{5} = \frac{2}{5}$ of the pizza is remaining.

Converting this to a percentage, we have:

$\frac{2}{5} = \frac{2}{5} \times 100\% = \frac{200}{5}\% = \boxed {\textbf {(C) } 40}\%$

~anabel.disher

Solution 2

Converting the amount of pizza that Ravindra ate into a percentage, we have $\frac{2}{5} = \frac{2}{5} \times 100\% = \frac{200}{5}\% = 40\%$ .

Since Hongshu ate half of that, he ate $40\% \div 2 = 20\%$ of the pizza.

Summing the percentages to see how much pizza they ate in total, we can see that they ate $40\% + 20\% = 60\%$ of the pizza in total.

Subtracting this from $100\%$ of the pizza, which is the whole pizza, we can see that $100\% - 60\% = \boxed {\textbf {(C) } 40}\%$ of the pizza remains.

~anabel.disher

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2006 CEMC Pascal Problems/Problem 6

Problem

Solution 1

Solution 2