Question 1129615: Use a system of linear equations with two variables and two equations to solve.
A moving company charges a flat rate of $120, and an additional $8 for each box. If a taxi service would charge $20 for each box, what is the minimum number of boxes you would need for it to be cheaper to use the moving company?
What would be the total cost?
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website! .
The system is
y = 120 + 8x, (1)
y = 20x, (2)
where x is the number of boxes and y is the total cost.
To solve the system, notice that the left sides of the two equations are identical - so their right sides should be equal:
120 + 8x = 20x (getting this equation is identical to substitution eq(1) into eq(2)).
Then
120 = 20x - 8x
12x = 120 ====> x = 120/12 = 10.
Answer. 10 boxes is break even. Moving company is cheaper if the number of boxes is 11 or greater.
Then the total cost by the moving company would be 120+11*8 = 208 dollars,
while by taxi it would be 11*20 = 220 dollars.
Notice : Usually (as a rule) such problems students solve using one single equation or inequality.
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