Question

1. joe earned $52.50 in interest on a 6 month investment at 7%. how much money did he invest? (hint: i = prt)
2. write 8:136 as a ratio in simplest form.
3. jennifer drove to cleveland to visit her sister at a rate of 65 mph. she returned home at a rate of 45 mph. if the entire trip took 10 hours, how long did it take her to get to cleveland?
4. colleen finished the first 15 problems of the final exam in 20 minutes. at that rate, how long will it take her to complete the 75 question final exam?
5. of a total of 504 seniors, 234 are boys. what is the ratio of the number of boys to the number of girls in the senior class?

Explanation:

Problem 46

Step1: Identify formula and values

Given \( I = prt \), \( I = 52.50 \), \( r = 7\%=0.07 \), \( t = 6 \) months \( = \frac{6}{12}=0.5 \) years.

Step2: Solve for \( p \)

Rearrange formula: \( p=\frac{I}{rt} \). Substitute values: \( p = \frac{52.50}{0.07\times0.5} \).

Step3: Calculate denominator

\( 0.07\times0.5 = 0.035 \).

Step4: Calculate \( p \)

\( p=\frac{52.50}{0.035}=1500 \).

Step1: Find GCD of 8 and 136

GCD of 8 and 136 is 8.

Step2: Divide both by GCD

\( \frac{8\div8}{136\div8}=\frac{1}{17} \), so ratio is \( 1:17 \).

Step1: Let time to Cleveland be \( t \)

Time to return is \( 10 - t \). Distance to Cleveland: \( d = 65t \), distance back: \( d = 45(10 - t) \).

Step2: Set distances equal

\( 65t = 45(10 - t) \).

Step3: Expand right side

\( 65t = 450 - 45t \).

Step4: Add \( 45t \) to both sides

\( 110t = 450 \).

Step5: Solve for \( t \)

\( t=\frac{450}{110}=\frac{45}{11}\approx4.09 \) hours (or \( 4 \) hours \( 5.45 \) minutes, but exact fraction is \( \frac{45}{11} \) or decimal \( \approx4.09 \)).

Answer:

\$1500

Problem 47