Henry needs to rent a moving truck. Suppose Company A charges a rate of $50 per day and Company B charges $70 fee plus $30 per day. For what number of days is the cost the same?

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Answer 1 · 2018-07-12T16:52:11

$3 \frac{1}{2} d a y s$ $3 1/2 days$

To solve this set Company A equal to Company B

Let $n = d a y s$ $n = days$

The cost for Company A is $$ 50 n$ $$50n$
The cost for Company B is $$ 70 + $ 30 n$ $$70 + $30n$

Set the equation $$ 50 n = $ 70 + $ 30 n$ $$50n = $70 + $30n$

$50 n = 70 + 30 n$ $50n = 70 + 30n$

Use additive inverse to combine the variable terms on one side of the equation.

$50n - 30n = 70 cancel(+ 30n) cancel(- 30n)$

$20n = 70$

Use multiplicative inverse to isolate the variable.

$(cancel20n)/cancel20 = 70/20$

$n =7/2$ or $3 1/2$