Ela has $6.40 in nickels and quarters. If she has 26 more nickels than quarters, how many of each coin does she have?

Question

if 0.05 x 26 equals to $1.30, how do i determine how many of each coin she has 

Answer 1

Hey Jack!

 

We first have to establish a system of equations. Since we have two unknown variables, we need to have two equations. The first equations;

 

5N+25Q=640

N=26+Q

 

Where N= number of nickels, Q=number of quarters. 

Note, I multiplied everything by 100 in the first equation because decimals can get lost sometimes! 

 

If I plug in for N, I get

 

5(26+Q)+25Q=640, Multiplied out gives us;

 

130+5Q+25Q=640, combine Q terms, and subtract 130 from both sides leaves;

 

30Q=510, divide by 30,

 

Q=17.

 

Now, take this Q=17 and plug in to the N= equation to solve for N.

 

N=26+(17)

 

N=43

 

A quick check can be made to make sure this is correct by;

 

0.05(43)+.25(17)=6.40

 

Hope this helps!

 

 

 

Answer 2

You have to write an equation with a variable and solve it

 

let x = number of quarters

x+26 = number of nickels

 

number of quarters times .25 plus number of nickels times .05 is 6.40

 

.25x + .05*(x+26) = 6.40