Question

BeginV number17.Kim starts with $500 and spends $15 per week. Her brother starts with $800and spends $35 per week.a. Write the expressions you would use to solve this equation:b. When does Kim have more money than Roy?

Answer 1

For Kim:

Since Kim starts with $500 and spents $15 per week, then

She has: 500 - 15x, where x is the number of weeks

For her brother:

Since her brother starts with $800 and spends $35 per week, then

He has 800 - 35x, where x is the number of weeks

a. The expressions are:

`\begin{gathered} 500-15x \\ 800-35x \end{gathered}`

If Kim has more than her brother, then we should write an inequality

`500-15x>800-35x`

Let us solve it to find the range of x

Add 35x to both sides

`\begin{gathered} 500-15x+35x>800-35x+35x \\ 500+20x>800 \end{gathered}`

Subtract 500 from both sides

`\begin{gathered} 500-500+20x>800-500 \\ 20x>300 \end{gathered}`

Divide both sides by 20

`\begin{gathered} (20x)/(20)>(300)/(20) \\ x>15 \end{gathered}`

x should be greater than 15

b. Kim has more money than Roy after 15 weeks