linear equation

Question

A parking meter contains nickels and quarters worth $10.25. There were 77 coins in all. Find how many of each there are 

 

How many nickels are there? =

How many Quarters are there?=

Answer 1

To solve this, we will need to use a system of equations. In systems of equations, we have 4 main steps: CREATE EQUATIONS, SOLVE FOR 1 VARIABLE, SUBSTITUTE ONE VARIABLE FOR ANOTHER, AND PLUG IN THE ANSWER.

 

So the EQUATION we get right from the question is

 

.05n + .25q=10.25

 

where n is the number of nickels and q is the number of quarters. Next, we know that there are 77 coins in total. So,

 

n+q=77

(or in English, the number of nickles plus the number of quarters equals 77)

 

The next step is to SOLVE for one of the variables

 

n+q=77

n=77-q

 

Step 3: we Substitute one of the variables. Our first equation was .05n +.25q=10.25. Since we know that n=77-q, let's substitute for n.

 

.05(77-q)+.25q=10.25

 

now we solve for q:

 

3.85-0.05q+.25q=10.25

3.85+.20q=10.25

.20q=6.4

q=32

 

So now we know there are 32 quarters. To find n we subtract 32 from 77

77-32=n

n=45

 

To check your answer, plug in the numbers we got for q and n and see if they give you 10.25!

 

Hope that helps,

Nikita