Jason has 20 coins that are only dimes and quarters. The total value is $2.75. How many of these are quarters?
I tried answering it but I got 5 quarters. I'm not so sure if that's the right answer. Can you show me the equation and the right answer to see if I'm correct? Thanks!
Let's start with your answer. Five quarters = $1.25. 2.75 - 1.25 = $1.50.
Fifteen dimes = $1.50.
Your answer is right.
To solve this problem, let's define some variables:
Let's say "x" represents the number of dimes, and "y" represents the number of quarters.
We know that Jason has a total of 20 coins, so we can write the following equation:
x + y = 20 (equation 1)
Next, we know that the total value of all the coins is $2.75. Dimes are worth $0.10 each, and quarters are worth $0.25 each. So, the equation representing the total value of the coins is:
0.10x + 0.25y = 2.75 (equation 2)
To find the number of quarters, we need to solve this system of equations (equation 1 and equation 2).
Using substitution method, let's solve equation 1 for x:
x = 20 - y
Now, substitute this into equation 2:
0.10(20 - y) + 0.25y = 2.75
Simplify:
2 - 0.10y + 0.25y = 2.75
0.15y = 0.75
y = 0.75 / 0.15
y = 5
So, the number of quarters, "y," is 5.
To double-check the answer, substitute this value of y back into equation 1:
x + 5 = 20
x = 15
Therefore, Jason has 15 dimes and 5 quarters, which adds up to 20 coins and a total value of $2.75.
So, your initial answer of 5 quarters is indeed correct.