Question

Chris earns four times Vesna's wage v and Vesna earns $17 more than Dawn. How many dollars does Chris earn if their combined wages are $163?

Answer 1

By setting up a system of equations with the given information, we find that Vesna earns $30 and Chris earns four times that amount, which means Chris's wage is $120.

Step-by-step explanation:

To solve the problem of how much Chris earns given the conditions in the question, we need to use a system of equations based on the information provided:

• Chris earns four times Vesna's wage (4v)
• Vesna earns $17 more than Dawn (v = d + 17)
• Their combined wages are $163 (4v + v + d = 163)

Since Vesna earns $17 more than Dawn, we can express Dawn's wage as (v - 17). Substituting Dawn's wage into the combined wages equation, we have (4v + v + (v - 17) = 163). Simplifying, we get 6v - 17 = 163. Adding 17 to both sides gives 6v = 180, and dividing by 6, we find v = 30. Now, we can calculate Chris's wage, which is four times Vesna's wage, so Chris earns 4 × 30 = $120.

Answer 2

Call Dawn's wage x, we will have Vesna's wage = x + 17 and Chris' wage = 4x(x + 17). So we have the equation:

`x + (x + 17) + 4 * (x + 17) = 163 \\ 2x + 17 + 4x + 68 = 163 \\ 6x = 78 \\ x = 13`
Therefore, Chris's wage:

`4 * (13 + 17) = 120`