SOLUTION: I know the result to this problem, but am having a hard time finding the equation that works for it. I spent 2 hours on it last night with no luck, can you help me please? The ques

Question 12603: I know the result to this problem, but am having a hard time finding the equation that works for it. I spent 2 hours on it last night with no luck, can you help me please? The question is as follows:
Abby has 37 coins, consisting only of dimes and quarters, woth $7.45. How many dimes and how many quarters does she have?
I know that she has 25 quarters and 12 dimes, but that is form simple math.
Thanks for the help!!
Capesch
Answer by AdolphousC(70) (Show Source): You can put this solution on YOUR website!
You need to set this up as a system of linear equations,
Define your varibles, Let D = # of Dimes, and Q = # of Quarters

First Equation is the one where you actually just count the coins...
D + Q = 37
Now, adding the value of the coins, here is where you count the money,
Dimes are worth 10 cents and quarters 25...
.1D + .25Q = 7.45

D + Q = 37
.1D + .25Q = 7.45

Now you have a simple system, I will multiply the top by .1
.1(D + Q = 37)
.1D + .25Q = 7.45

.1D + .1Q = 3.7
.1D + .25Q = 7.45 Now subtract the two equations

-.15Q = -3.75 Divide both sides by -.15
Q = 25

Now substitute into your original equations
D + Q = 37
D + 25 = 37 Subtract
D = 12

So she indeed has 25 Quarters and 12 Dimes

RELATED QUESTIONS
Hi, I am trying to find the function rule for the following table: x: 2, 4, 6 y: 1, 0,... (answered by josgarithmetic,richwmiller,rothauserc)

James can paint a room in 4 hours, while Mike can paint the same room in 5 hours. Working (answered by josgarithmetic)

I am trying to write an equation of the line that passes through these points (-1,3) and... (answered by oberobic)

Hi thank you for aking the time to helpme with this, I have a writingassignment and I... (answered by ankor@dixie-net.com)

I am having a hard time with right triangles and finding the measures for them if the are (answered by josgarithmetic)

I am having problems with this problem as I am having a very hard time grasping the... (answered by Nate,lomlheather)

I am having problems with this problem as I am having a very hard time grasping the... (answered by stanbon)

Factor: 42-13r+r^2 I don't even know where to begin with this problem! I am also... (answered by jim_thompson5910)

I'm having a problem with this world problem finding an equation for it. I was able to... (answered by nerdybill,Alan3354)