Afamily has two cars. the first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. during one particular week, the two cars went a combined total of 850 miles, for a total gas consumption of 50 gallons. how many gallons were consumed by each of the two cars that week?

Let the number of gallons consumed be the first car be x, and that of the second car, y. Then:
x + y = 50 . . . . . . . (1)
20x + 15y = 850. . . (2)

(1) x 20 => 20x + 20y = 1000 . . . (3)
(2) - (3) => -5y = -150 => y = -150/-5 = 30

From (1), x + 30 = 50 => x = 50 - 30 = 20

Therefore, first car consumed 20 gallons and the second consumed 30 gallons.

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