Question

Bella and Heather put some money into their money boxes every week. The amount of money (y), in dollars, in their money boxes after a certain amount of time (x), in weeks, is shown by the equations below:

Bella: y = 25x + 60
Heather: y = 30x + 10

After how many weeks will Bella and Heather have the same amount of money in their money boxes, and what is that amount? (4 points)


A. 10 weeks, $10

B. 10 weeks, $310

C. 9 weeks, $310

D. 310 weeks, $10

Answer 1

`\boxed{ \text{B. 10 weeks, \$310 }}\\`

Explanation:

We have two conditions:

`\begin{array}{lrcll}(1) & y & = & 25x + 60 & \\(2) & y & = & 30x + 10 & \\ & 25x + 60 & = & 30 x + 10 & \text {Set (1) = (2)} \\ & 50 & = & 5x & \text{Subtracted 25x from each side} \\& x & = & 10 &\text{Divided each side by 5} \\\end{array}\\$ $\\\boxed{ \textbf{The number of weeks is }x = 10}\\`

Bella: y = 25x + 60 = 25(10) + 60 = 250 + 60 = 310

Heather: y = 30x + 10 = 30(10) + 10 = 300 + 10 = 310