I need help with a math problem?
January 15, 2012 by Admin
Filed under Discussions
In a family there are two cars. The sum of the average miles per gallon Obtained by the two cars in a Particular week is 55th The first car has consumed 35 gallons during that week, and the second has consumed 40 gallons, for a total of 2000 miles driven by the two cars combined. What was the average gas mileage Obtained by each of the two cars in that week?
mpg1 + mpg2 = 55 => 35 mpg1 + 35 mpg2 = 1925
mpg1 * 35 + mpg2 * 40 = 2000
5 mpg2 = 75
mpg2 = 15 => mpg1 = 40
Let x = mpg for car #1
Let y = mpg for car #2
Since the problem states that the mpg sums to 55, we have the following:
x + y = 55
We are also told that they consume 35 and 40 gallons. So we can write this equation.
35x + 40y = 2000
Therefore, we have the following system of equations:
{ x + y = 55
{ 35x + 40y = 2000
I’ll solve by subsitution.
x + y = 55
==> x = 55 – y
35x + 40y = 2000
==> 35(55 – y) + 40y = 2000
==> 1925 – 35y + 40y = 2000
==> 1925 + 5y = 2000
==> 5y = 75
==> y = 15
Subsituting 13 as y into equation 1 gives us:
x + y = 55
==> x + 15 = 55
==> x = 40
Therefore, the cars got 40mpg and 15mpg.
Check:
-> x = 40, y = 15 < -
x + y = 55
==> 40 + 15 = 55
==> 55 = 55 (True)
35x + 40y = 2000
==> 35(40) + 40(15) = 2000
==> 1400 + 600 = 2000
==> 2000 = 2000 (True)
Therefore, it checks.
Hope this helps.