Answer: There are 18 nickels and 22 quarters
Step-by-step explanation:
Notice that nickels are worth 5 cents and quarters are worth 25 cents.
We will develop two equations using the given information. the number of nickels will be represented by x and the number of quarters will be represented by y.
5 cent is the same as 0.05
and 25 cents is the same as 0.25
0.05x + 0.25y = 6.40 This equal can be used to model the first statement.
There are forty collection which means a combination of nickels and quarters has to equal 40 and that can also be represented by the equation x +y=40
0.05x + 0.25y = 6.40
x + y = 40
Using both equations, we can solve for x and y using the elimination method.
To eliminated the x variable multiply the down equation by -0.05.
-0.05(x+y) = -0.05(40) Multiply to get the new equation ,
-0.05x - 0.05y = -2
Combine the first equation with the new equation.
0.05x + 0.25y = 6.40
-0.05x - 0.05y = -2 Add both equations
0.2y = 4.4
y= 22
This means that there are 22 quarters and to find the number of nickels we will subtract 22 from 40.
40 -22 = 18
There are 18 nickels
