Question

Prove that it is impossible to have $4.50 in dimes and quarters with the number of quarters being twice the number of dimes

Answer 1

To prove that it is impossible to have $4.50 in dimes and quarters with the number of quarters being twice the number of dimes, we can set up a system of equations and solve for the variables. However, we find that the number of dimes is not a whole number, making it impossible.

Step-by-step explanation:

To prove that it is impossible to have $4.50 in dimes and quarters with the number of quarters being twice the number of dimes, we can set up a system of equations.

Let x represent the number of dimes and y represent the number of quarters.

The value of the dimes would be 0.10x and the value of the quarters would be 0.25y.

We are given that the number of quarters is twice the number of dimes, so we have the equation y = 2x.

The total value of the coins is $4.50, so we have the equation 0.10x + 0.25y = 4.50.

Substitute y = 2x into the second equation:

0.10x + 0.25(2x) = 4.50

0.10x + 0.50x = 4.50

0.60x = 4.50

x = 7.5

This means that the number of dimes, x, is 7.5. However, the number of dimes has to be a whole number, so it is impossible to have $4.50 in dimes and quarters with the number of quarters being twice the number of dimes.

Answer 2

See Explanation below for proof.

Step-by-step explanation:

Let number of dimes be D

Then number of quarters = 2D

We then get the following VALUE equation: .1D + .25(2D) = 4.5

.1D + .5D = 4.5

.6D = 4.5

D, or number of dimes = 4.5/.6 = 7.5

There is no such thing as HALF a DIME, so it's NOT POSSIBLE