Sally has $21.40 in dimes and quarters, for a total of 100 coins. How many of each kind of coin does sally have?

Question

I have a quiz tomorrow and I need to do well

Answer 1

The way you approach this kind of problem is by creating a system of equations. (I'm assuming you're in Algebra class, yes?)

 

Your first equation uses the number of coins values. Your second uses all the $ values.

 

So. You note that you have dimes and quarters. You set up two variables:

 

D = number of dimes

Q = number of quarters

 

Your first equation uses the total number of coins.

 

eq. 1:   D + Q = 100   (this is all number of coins)

 

Now you need your $ values equation. Dimes are worth $.10, and quarters are worth $.25. You have a total dollar value of $21.40.

 

Multiply the number of dimes, D, by their value, giving $.10D. Multiply the number of quarters by their dollar value... that's $.25Q. Add them... and they total the total dollar value. That's your second equation:

 

.10D + .25Q = 21.40   (you can leave the $ signs out now, since they're on both sides.)

At this point I like to get rid of the decimal points, because they are "messy". You don't have to, but it's easier if you do. Just multiply each value by 100... moving the decimal point two places to the right. This gives you:

 

eq. 2:  10D + 25Q = 2140

 

So, now solve the system of equations. You can do this by elimination or substitution, whichever you like.

 

By elimination, you'd multiply equation 1 by -10, and then add the two equations together:

 

eq. 2:   10D + 25Q = 2140

eq. 1: -10D -10Q = -1000

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                   15Q = 1140,  Q = 76

D+Q=100;D+76=100;D=24

 

By substitution you would solve the original eq1 for either D or Q and sub that into eq2, and I'll leave that for you if you like to do the problems that way.

 

--LouiseK

 

 

 

 

 

 

Answer 2

1 dime = $0.1 

A quarter =$0.25

let there be X dimes and Y quarters

Given X+y =100

Xx0.1 +yYx0.25 =21.40

Solving these two equations

10X =25Y = 2140

X +y + 100

 

X =24

 Y =76

Ans 24 dimes and 76 quarters