Question

type the correct answer in each box.
the brown family needs to rent a truck for their upcoming move. express movers will charge them $25 for the first day and $0.80 for every mile. smith & smith co. will charge $35 for the first day and $0.60 for every mile. before deciding which service to use, mrs. brown wants to find out how many miles would make the two choices equivalent in cost. the following equations represent this situation.
$y = \frac{4}{5}x + 25$
$y = \frac{3}{5}x + 35$
here, $x$ represents number of miles and $y$ represents the cost
this situation is shown in the graph.
(graph with y-axis labeled dollars (cost) and x-axis for miles, showing two lines intersecting)

Explanation:

Step1: Set equations equal

To find when costs are equal, set \(\frac{4}{5}x + 25=\frac{3}{5}x + 35\).

Step2: Subtract \(\frac{3}{5}x\)

\(\frac{4}{5}x-\frac{3}{5}x + 25=\frac{3}{5}x-\frac{3}{5}x + 35\) simplifies to \(\frac{1}{5}x + 25 = 35\).

Step3: Subtract 25

\(\frac{1}{5}x + 25 - 25=35 - 25\) gives \(\frac{1}{5}x = 10\).

Step4: Multiply by 5

Multiply both sides by 5: \(x = 50\).

Answer:

50