Question

percents

1. 98 is what percent of 58?
2. what is 87% of 54?
3. 105 is 6% of what?
4. a company made $800 one - week and $900 the next. what was the percent increase?
5. a couch normally costs $630 but was on sale for $575. what was the percent discount?
6. a chair sold for $267.05. this was after a 25% discount. what was the original price before the sale?
7. after a 20% tip was added on to the cost of a meal, the total bill was $45.98. what was the original cost of the meal?

proportions

1. a 6 ft tall boy casts a shadow 3 feet long. how long is the shadow of a 18 ft tall tree?
2. there are two similar triangles. one has sides 4 ft, 11 ft, 13 ft, and the corresponding side of the other are 12 ft, x, and y. find x and y.

Explanation:

34. 38 is what percent of 58?

Step1: Set up the proportion

Let $p$ be the percentage. The proportion is $\frac{38}{58}=\frac{p}{100}$.

Step2: Cross - multiply

$38\times100 = 58p$. So, $3800=58p$.

Step3: Solve for $p$

$p=\frac{3800}{58}\approx65.52\%$.

Step1: Convert percentage to decimal

$87\% = 0.87$.

Step2: Multiply

$0.87\times54 = 46.98$.

Step1: Let the number be $x$.

Set up the equation $105 = 0.06x$.

Step2: Solve for $x$

$x=\frac{105}{0.06}=1750$.

Answer:

Approximately $65.52\%$

35. What is 87% of 54?