Question

A collection of nickels and dimes is worth $9.45. If the number of dimes is doubled, the value is

Answer 1

Answer:

The number of nickels is 45 and the number of dimes is 72.

Step-by-step explanation:

Let

x ----> number of nickels

y ----> number of dimes

Remember that

$1\ nickel=\ 0.05$

$1\ dime=\ 0.10$

so

$0.05x+0.10y=9.45$ ------> equation A

$0.05x+0.10(2y)=16.65$

$0.05x+0.20y=16.65$ ------> equation B

Solve the system by substitution

we have

$0.05x+0.10y=9.45$ ------> equation A

$0.05x+0.20y=16.65$ ------> equation B

Multiply both equations by 100 both sides

$5x+10y=945$ ---->$5x=945-10y$ --> equation C

$5x+20y=1,665$ ----> equation D

substitute equation C in equation D

$(945-10y)+20y=1,665$

solve for y

$945+10y=1,665$

$10y=1,665-945$

$10y=720$

$y=72\ dimes$

Find the value of x

$5x=945-10y$

$5x=945-10(72)$

$5x=225$

$x=45\ nickels$

Alternative Method

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

the solution is the point (45,72)

therefore

The number of nickels is 45 and the number of dimes is 72.