Arithmetic › Percentages

Comparing percentages

Solve the first problem 18 problems

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1. Unknown number from percentages ●○○○○ 10 ptsIf $15\%$ of $N$ is $45\%$ of $2003$, what is the value of $N$?
2. Percentage relation between three quantities ●○○○○ 10 ptsIf $x$ is $20\%$ of $y$ and $x$ is $50\%$ of $z$, then what percentage is $z$ of $y$?
3. Percent relation through a common third number ●○○○○ 10 ptsTwo numbers are respectively 20% and 25% of a third number. What percentage is the first number of the second number?
4. Share of total area from rose fractions ●●○○○ 20 ptsTwo fields are planted with roses and lavender. $65\%$ of the area of the first field is roses, $45\%$ of the area of the second field is roses, and $53\%$ of the area of both fields together is roses. What percentage of the total area (of both fields together) is the area of the first field?
5. Two equations with percents ●●○○○ 20 ptsThe sum of $x$ and $y$ is 150. The sum of 5 percent of $x$ and 10 percent of $y$ is 11. Find $x$ and $y$.
6. Two numbers with a percent relation ●●○○○ 20 ptsThe sum of two numbers is 4000. $15\%$ of one number equals $25\%$ of the other number. Find the two numbers.
7. Percent of A and A+B equal ●●●○○ 50 ptsLet $A$ and $B$ be positive numbers. $B$ as a percent of $A$ is equal to $A$ as a percent of $(A+B)$. Find $B$ as a percent of $A$. Round to the nearest whole percent.
8. Least integer with percentage conditions ●●●○○ 50 ptsLet $N$ be the least positive integer that is both 22 percent less than one integer and 16 percent greater than another integer. Find the remainder when $N$ is divided by 1000.

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