A family has two cars. The first car has a fuel efficiency of

30
miles per gallon of gas and the second has a fuel efficiency of

40
miles per gallon of gas. During one particular week, the two cars went a combined total of

1700
miles, for a total gas consumption of

50
gallons. How many gallons were consumed by each of the two cars that week

Question

A family has two cars. The first car has a fuel efficiency of 



30
 miles per gallon of gas and the second has a fuel efficiency of 



40
 miles per gallon of gas. During one particular week, the two cars went a combined total of 



1700
 miles, for a total gas consumption of 



50
 gallons. How many gallons were consumed by each of the two cars that week

anonymous · Answer

@misty1212  I need help :(((( with a few word problems like this :(

misty1212 · Answer

HI!!

misty1212 · Answer

i hate word problems don't you?

misty1212 · Answer

we need a variable, maybe two or we could get away with one, your choice

anonymous · Answer

ugh yes I hate this dislike them basically I just don't like them in general :( @misty1212

dan815 · Answer

i love them :)

misty1212 · Answer

ok say $x$ is the distance travelled by the 30 mph car and y the distance traveled by the 40 mph car
then we can make two equations 
$$x+y=1700$$ is the easy one

misty1212 · Answer

the amount of gas used by the 30 mph car is $\frac{x}{30}$ and the amount used by the 40 mph car is $\frac{y}{40}$ so the next equation is 
$$\frac{x}{30}+\frac{y}{40}=50$$

misty1212 · Answer

you know how to solve that system?
$$x+y=1700\
\frac{x}{30}+\frac{y}{40}=50$$