Question

there are nickels, dimes, and quarters in a piggy bank. altogether, the coins are worth $3.65. the number of dimes is three times greater than the number of nickels, and the number of quarters is one greater than double the number of nickels. how many quarters, nickels, and dimes are there?

Answer 1

This question is solved using a system of equations, and doing this, we get that: There are 9 quarters, 4 nickels and 12 dimes.

I am going to say that:

x is the number of nickels.

y is the number of dimes.

z is the number of quarters.

In all, they are worth $3.65.

A nickel is worth $0.05, a dime is worth $0.1 and a quarter is worth $0.25, so:

$0.05x + 0.1y + 0.25z = 3.65$

Dimes: 3 times greater than nickels:

This means that:

$y = 3x$

Quarters: One greater than double the number of nickels:

This means that:

$z = 2x + 1$

Value of x:

We have y and z as function of x, so we can replace into the equation and find the value of x, so:

$0.05x + 0.1y + 0.25z = 3.65$

$0.05x + 0.1(3x) + 0.25(2x+1) = 3.65$

$0.05x + 0.3x + 0.5x + 0.25 = 3.65$

$0.85x = 3.4$

$x = \frac{3.4}{0.85}$

$x = 4$

y and z:

$y = 3x = 3(4) = 12$

$z = 2x + 1 = 2(4) + 1 = 9$

There are 9 quarters, 4 nickels and 12 dimes.

A similar question is found at brainly.com/question/17096268