Question

**WILL MEDAL**
A container holds a combination of dimes and quarters. There are 178 coins in all, and their total value is $29.80. The system of equations models this situation, where x is the number of dimes and y is the number of quarters.
x+y=178
0.1x+0.25y=29.8


How many dimes and quarters are in the container?

A.
123 dimes and 55 quarters

B.
114 dimes and 64 quarters

C.
102 dimes and 76 quarters

D.
98 dimes and 80 quarters

Answer 1

Use the process of elimination to find the number of each since you're already given two equations. You're going to have to eliminate one variable and solve for the other one.

Say you want to find the number of quarters first, y.

Answer 2

x+y=178
0.1x+0.25y=29.8

We'd have to first eliminate x. In order to do that we need to multiply the first equation by -0.1

-0.1(x + y =178)
0.1x +0.25y = 29.8
_______________________

-0.1x -0.1y = -17.8
0.1x +0.25y = 29.8
________________________ Now you just add them together

Answer 3

0x +y(0.25 -0.1) = 29.8 -17.8

0.15y = 12.0

y = 12.0/0.15

y = 80 quarters.

Now that we've found out one of the two, we can find # of dimes, x.

Answer 4

To do that,we can use either of the two equations, preferably the first one because it's easier to compute. Then we just plug in the amount of quarters we found and we can find the number of dimes :)

x + y = 178

x + 80 = 178

x = 178 - 80 = # of quarters

Answer 5

Ok thx I understand now how to do the next questions(:

Answer 6

*equation

Answer 7

Awesome! :D