Question 1

Jessica has $14500 to invest and decides to put some in a CD that earns 1.5% interest per year and the rest in a low risk stock that earns 1.8%. How much did she invest to earn $247.65 interest in the first year?
A) $7,504.55 at 1.5% and $6,995.45 at 1.8%
B) $10,050 at 1.5% and $4,450.00 at 1.8%
C) $4,450.00 at 1.5% and $10,050 at 1.8%
D) $6,995.45 at 1.5% and $7,504.55 at 1.8%

Accepted Answer

The answer of Jessica has $14500 to invest and decides...

Question 2

A motorboat can maintain a constant speed of 11 miles per hour relative to the water. The boat makes a trip upstream in 41 minutes and the return trip takes 22 minutes. What is the speed of the current?
A) 0.3 mph
B) 11 mph
C) 3.3 mph
D) 22 mph

Accepted Answer

The speed of the boat relative to the water is 11 mph. Let the speed of the current be $c$ mph. When going upstream, the effective speed of the boat is $11 - c$ mph, and when going downstream, it's $11 + c$ mph. The time taken for the upstream trip is 41 minutes ($\frac{41}{60}$ hours) and for the downstream trip is 22 minutes ($\frac{22}{60}$ hours). Let the distance of the trip in one direction be $d$ miles. We can set up the equations based on the formula $distance = speed \times time$:For upstream: $d = (11 - c) \times \frac{41}{60}$For downstream: $d = (11 + c) \times \frac{22}{60}$Since the distances are the same, we can set the expressions equal to each other and solve for $c$:$(11 - c) \times \frac{41}{60} = (11 + c) \times \frac{22}{60}$Solving this equation gives $c = 3.3$ mph.

Question 3

Lee can mow a lawn in 30 minutes. It takes Ito 50 minutes to mow a lawn of the same size. How long would it take them to mow the lawn if they work together?
A) 40.0 minutes
B) 20 minutes
C) 18.7 minutes
D) 80 minutes

Accepted Answer

Lee's rate is 1/30 of the lawn per minute, and Ito's rate is 1/50 of the lawn per minute. Working together, their combined rate is 1/30 + 1/50 = 5/150 + 3/150 = 8/150 = 4/75 of the lawn per minute. To find the time it takes to mow the entire lawn, take the reciprocal of their combined rate: 75/4 = 18.75 minutes.

Question 4

The length of a rectangle is 5 feet more than 5 times its width. The perimeter of the rectangle is 202 feet. What is the length of the rectangle?

Accepted Answer

The answer of The length of a rectangle is 5...

Quiz 12: Review: Equations and Inequalities

Jessica has $14500 to invest and decides to put some in a CD that earns 1.5% interest per year and the rest in a low risk stock that earns 1.8%. How much did she invest to earn $247.65 interest in the first year?

A motorboat can maintain a constant speed of 11 miles per hour relative to the water. The boat makes a trip upstream in 41 minutes and the return trip takes 22 minutes. What is the speed of the current?

Lee can mow a lawn in 30 minutes. It takes Ito 50 minutes to mow a lawn of the same size. How long would it take them to mow the lawn if they work together?

The length of a rectangle is 5 feet more than 5 times its width. The perimeter of the rectangle is 202 feet. What is the length of the rectangle?