Question

q. jaquez is saving money to buy a boat. he made an initial deposit of $800 and has since saved 35% of the remaining cost of the boat. if he has saved $1,400, how much does the boat cost?

a. $4,000
b. $4,800
c. $5,200
d. $5,600

Explanation:

Define variables for the boat cost

Let \(C\) represent the total cost of the boat in dollars.
The remaining cost of the boat after the initial deposit of \(\$800\) is:

$$R = C - 800$$

Set up the savings equation

Using the Word Problems knowledge point, we translate the given information into an equation.
Jaquez made an initial deposit of \(\$800\) and has since saved \(35\%\) of the remaining cost \(R\).
His total savings is \(\$1,400\).
The total amount saved is the sum of the initial deposit and the subsequent savings:

$$800 + 0.35(C - 800) = 1400$$

Solve for the remaining cost

Subtract \(800\) from both sides of the equation to isolate the term representing the subsequent savings:

$$0.35(C - 800) = 600$$

Divide both sides by \(0.35\) to find the remaining cost:

$$C - 800 = \frac{600}{0.35}$$

$$C - 800 = \frac{60000}{35} = \frac{12000}{7} \approx 1714.29$$

Let's re-evaluate the phrasing: "If he has saved \$1,400" could mean his *since saved* amount is \$1,400, or his total saved amount is \$1,400.
If "he has saved \$1,400" refers to the amount saved since the deposit:

$$0.35(C - 800) = 1400$$

$$C - 800 = \frac{1400}{0.35}$$

$$C - 800 = 4000$$

$$C = 4800$$

This yields exactly \(\$4,800\), which is option B.

If "he has saved \$1,400" refers to his total savings:

$$\text{Total saved} = 800 + 0.35(C - 800) = 1400 \implies 0.35(C - 800) = 600 \implies C - 800 \approx 1714.29 \implies C \approx 2514.29$$

This value is not among the choices. Thus, "has saved \$1,400" refers to the amount saved since the initial deposit.

Calculate the total cost of the boat

Using the correct interpretation where the subsequent savings equal \(\$1,400\):

$$C = 4000 + 800 = 4800$$

The total cost of the boat is \(\$4,800\).

Answer:

• (A) $4,000
• (B) $4,800 (Correct answer)
• (C) $5,200
• (D) $5,600