Question

the price for video game a is $18 more than the price for video game b. if the total of these two prices is $52, find the price of each game.

the cost for video game a is $ and the cost for video game b is $
(type integers or decimals.)

Explanation:

Define variables for game prices

Let \(A\) be the price of video game A in dollars.
Let \(B\) be the price of video game B in dollars.

Set up the system of equations

The first relation states game A is \$18 more than game B:

$$A = B + 18$$

The second relation states the total price is \$52:

$$A + B = 52$$

Substitute and solve for B

Substitute the first equation into the second equation:

$$(B + 18) + B = 52$$

$$2B + 18 = 52$$

$$2B = 34$$

$$B = 17$$

Solve for A

Use the value of \(B\) to find \(A\):

$$A = 17 + 18$$

$$A = 35$$

Verify the solution

Check if the sum equals \$52:

$$35 + 17 = 52$$

The values are correct.

Answer:

The cost for video game A is $35 and the cost for video game B is $<blank>17</blank>