Solving Systems by Substitution
Maribel has $1.25 in her pocket. The money is in quarters and dimes. There are a total of 8 coins. How many quarters and dimes does Maribel have in her pocket?
I think the equation is 10x+25x=$1.25 and x+x=8 but I'm not sure.
Q+D=8
25Q+ 10D=125
Q+ D=8
multiply the second equation by 10
25Q+ 10D=125
10Q+ 10D=80
subtract the second equation from the first.
15Q=45
Q=3
then D=5
You're on the right track, but let's break it down step by step to solve the system of equations by substitution.
Step 1: Identify the variables:
Let's assume that x represents the number of dimes and y represents the number of quarters in Maribel's pocket.
Step 2: Set up the equations:
We know that the total value of the coins is $1.25, which can be expressed as:
0.10x + 0.25y = 1.25 (equation 1)
We also know that there are a total of 8 coins, so the number of dimes (x) plus the number of quarters (y) equals 8:
x + y = 8 (equation 2)
Step 3: Solve for one variable in terms of the other:
Let's solve equation 2 for x:
x = 8 - y
Step 4: Substitute the expression for x into equation 1:
0.10(8 - y) + 0.25y = 1.25
Step 5: Simplify and solve for y:
0.80 - 0.10y + 0.25y = 1.25
0.15y = 0.45
y = 0.45 / 0.15
y = 3
Step 6: Find the value of x:
Now that we know y = 3, we can substitute it back into equation 2 to find x:
x + 3 = 8
x = 8 - 3
x = 5
Thus, there are 5 dimes and 3 quarters in Maribel's pocket to make a total of 8 coins.