Question

Anthony has been saving nickels dimes quarters over the last year he knows that he has twice as many nickels as quarters. changes the coins to the change machine to exchange then for paper money. He learns that he has 260 coins totaling 29.75. The number of each type of coin Anthony saved. Fill in the blanks

Answer 1

The number of nickel's coin is 150

The number of dime's coin is 35

The number of quarter's coin is 75

Explanation:

Let

x ----> the number of nickel's coin

y ---> the number of dime's coin

z ---> the number of quarter's coin

Remember that

`1\ nickel=\$0.05`

`1\ dime=\$0.10`

`1\ quarter=\$0.25`

we know that

`x+y+z=260` ----> equation A

`0.05x+0.10y+0.25z=29.75` ----> equation B

`x=2z` ----> equation C

substitute equation C in equation A and equation B

`2z+y+z=260`

`3z+y=260` ---> equation A1

`0.05(2z)+0.10y+0.25z=29.75`

`0.35z+0.10y=29.75` -----> equation B1

Solve the system of equations A1 and B1 by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (75,35)

see the attached figure

so

z=75, y=35

Find the value of x

`x=2(75)=150`

therefore

The number of nickel's coin is 150

The number of dime's coin is 35

The number of quarter's coin is 75