Question

1. the lee family buys a new car that has a sales price of $35,000. if the car dealer requires a minimum down payment of 15%, what is the minimum down payment the lees must pay for their car?14. select all the expressions that are equivalent to $24x + 12$.$2(12x + 6)$$-6(-4x - 2)$$-3(8x - 4)$$12(1 + 2x)$$-4(-6 - 3x)$15. james borrows $4,200 to pay his college tuition. he signs a 5-year simple interest loan. if the monthly payments are $78.40, what is the interest rate on the loan?a 2%b 2.4%c 3%d 3.2%

Explanation:

Question 13

Step1: Convert percentage to decimal

$15\% = 0.15$

Step2: Calculate down payment

$\$35,000 \times 0.15$

Expand each expression to compare with $24x + 12$:

1. $2(12x + 6) = 24x + 12$ (equivalent)
2. $-6(-4x - 2) = 24x + 12$ (equivalent)
3. $-3(8x - 4) = -24x + 12$ (not equivalent)
4. $12(1 + 2x) = 12 + 24x = 24x + 12$ (equivalent)
5. $-4(-6 - 3x) = 24 + 12x = 12x + 24$ (not equivalent)

Step1: Calculate total amount paid

Total months = $5 \times 12 = 60$
Total payment = $\$78.40 \times 60 = \$4,704$

Step2: Calculate total interest

Interest = $\$4,704 - \$4,200 = \$504$

Step3: Use simple interest formula

Simple interest formula: $I = P \times r \times t$
Rearrange to solve for $r$: $r = \frac{I}{P \times t}$
Substitute values: $r = \frac{504}{4200 \times 5}$

Step4: Compute interest rate

$r = \frac{504}{21000} = 0.024 = 2.4\%$

Answer:

$\$5,250$

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Question 14