Question

1. cristian is saving money to buy a new computer. he saves the same amount of money each week.

• after 2 weeks of saving, he still needs $680 to buy the computer
• after 6 weeks of saving, he still needs $440 to buy the computer

how much does the computer cost?

Explanation:

Step1: Define variables

Let \( x \) be the weekly savings amount and \( C \) be the cost of the computer. After 2 weeks, the amount saved is \( 2x \), so \( C - 2x = 680 \). After 6 weeks, the amount saved is \( 6x \), so \( C - 6x = 440 \).

Step2: Subtract the two equations

Subtract the second equation from the first: \((C - 2x) - (C - 6x) = 680 - 440\). Simplify: \( C - 2x - C + 6x = 240 \), so \( 4x = 240 \).

Step3: Solve for x

Divide both sides by 4: \( x = \frac{240}{4} = 60 \).

Step4: Find C

Substitute \( x = 60 \) into \( C - 2x = 680 \): \( C - 2(60) = 680 \), so \( C - 120 = 680 \). Add 120 to both sides: \( C = 680 + 120 = 800 \).

Answer:

The computer costs \$800.