Question

practice and problem - solving exercises
a practice

1. business a bicycle store costs $2400 per month to operate. the store pays an average of $60 per bike. the average selling price of each bicycle is $120. how many bicycles must the store sell each month to break even?
2. theater producing a musical costs $88,000 plus $5900 per performance. one sold - out performance earns $7500 in revenue. if every performance sells out, how many performances are needed to break even?
3. investment you split $1500 between two savings accounts. account a pays annual 5% interest and account b pays 4% annual interest. after one year, you have earned total of $69.50 in interest. how much money did you invest in each account? expl

Explanation:

Problem 7

Step1: Define break-even condition

Total Revenue = Total Cost
Let $x$ = number of bicycles.
Total Cost = Fixed Cost + Variable Cost = $2400 + 60x$
Total Revenue = $120x$
Set equal: $120x = 2400 + 60x$

Step2: Isolate $x$ term

Subtract $60x$ from both sides:
$120x - 60x = 2400$
$60x = 2400$

Step3: Solve for $x$

Divide both sides by 60:
$x = \frac{2400}{60}$

Step1: Define break-even condition

Total Revenue = Total Cost
Let $x$ = number of performances.
Total Cost = Fixed Cost + Variable Cost = $88000 + 5900x$
Total Revenue = $7500x$
Set equal: $7500x = 88000 + 5900x$

Step2: Isolate $x$ term

Subtract $5900x$ from both sides:
$7500x - 5900x = 88000$
$1600x = 88000$

Step3: Solve for $x$

Divide both sides by 1600:
$x = \frac{88000}{1600}$

Step1: Define variables

Let $x$ = amount invested in Account A (5% interest).
Let $1500 - x$ = amount invested in Account B (4% interest).
Total interest = Interest from A + Interest from B = $69.50$

Step2: Set up interest equation

Interest = Principal × Rate, so:
$0.05x + 0.04(1500 - x) = 69.50$

Step3: Expand and simplify

$0.05x + 60 - 0.04x = 69.50$
$0.01x + 60 = 69.50$

Step4: Solve for $x$

Subtract 60 from both sides:
$0.01x = 9.50$
Divide by 0.01:
$x = 950$

Step5: Find amount for Account B

$1500 - x = 1500 - 950 = 550$

Answer:

40 bicycles

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Problem 8