Michael has 27 coins in all, valuing $4.50. If he only has quarters and dimes. How many of each kind does he have?

Question

this is a system of an equation word problem i want you to give me the equation and the solution also give me the steps

Answer 1

Let Q = number of quarters

Let D = number of dimes.

Then one equation must be:

D + Q = 27 (there are a total of 27 coins).

The value of a dime is 10 cents, so if Michael has D dimes, the value of those dimes is 10D cents.

The value of a quarter is 25 cents. If Michael has Q quarters the value of them is 25Q cents.

That means the 2nd equation is:

10D + 25Q = 450 (note that $4.50 has been converted to 450 cents).

The easiest way to solve this system is using the substitution method (because it is easy to isolate a variable from the 1st equation).

Since D + Q = 27, Q = 27 - D. Substitute that expression for Q into the 2nd equation.

10D + 25(27 - D) = 450

Now solve for D (the number of dimes).

10D + 675 - 25D = 450

-15D + 675 = 450

225 = 15D

D = 15

So,

Q = 27 - 15 = 12

Check:

10(15) = 150cents = $1.50

25(12) = 300cents = $3.00

And the total is $4.50 !