Question

Can anyone help me answer this?

Answer 1

A family has two cars. The first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1275miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?

Answer 2

This can be solved with a system of linear equations. Let x be the number of miles driven by the first car and let y be the number of miles driven by the second car. If we add x and y, we should have the total number of miles driven that week. So, x+y=1275. We also know how many miles per gallon each car uses. So, the number of miles driven times the number of miles per gallon should give how much gas each car used. So, 15x+30y=50. You can use either elimination or substitution to solve for x and y. Can you solve the equations from here?

Answer 3

So I use both x+y=1275 and 15x+30y=50

Answer 4

And use either substitution or elimination and that will give me the answer?

Answer 5

I need two answers though. First car gallons and second car

Answer 6

@SBurchette

Answer 7

The second equation I gave might be wrong, I'm looking the question over to make sure I have it written correctly.

Answer 8

If you give me both answers, i'll give you a medal?? woo haha :)

Answer 9

So, the second equation should actually be x/15 + y/30 = 50. If we use elimination to solve the system, we can multiply both sides of the equation x/15+y/30=50 by -15 to get -x - y/2=-750. Adding this equation to x+y=1275, we get y/2=525. So, y=1050. We can now substitute this into the first equation, x+y=1275 to get x+1050=1275. So, x=225. This means that the first car was driven 225 miles and the second car was driven 1050 miles.

Answer 10

It asks for the amount of gallons consumed by each car, not this miles?

Answer 11

Is it still the same answer or is that wrong

Answer 12

I misread that. So, now that we know that the first car was driven 225 miles and it get 15 miles to the gallon, we divide 225 by 15 and get that it used 15 gallons. Because the second car was driven 1050 miles and the car gets 30 miles to the gallon, we divide 1050 by 30 and get that the second car used 35 gallons.

Answer 13

Okay! Thanks so much. I won't find out if it's right until I finish the rest of the problems. but i'm sure it is. Thanks for helping i really appreciate it

Answer 14

No problem =)