if you have 15 coins in a bag and their total amount is $2.70 how many quarters and dimes are in the bag? Use substitution to solve
q+d=15
.25q+.10d=2.70
d=15-q
.25q+.10(15-q)=2.70
.25q+1.50-.10q=2.70
.25q-.10q=1.20
.15q=1.20
q=8
q+d=15
8+d=15
d=15-8
d=7
d stands for dimes
q stands for quarters
To solve this problem using substitution, let's assign variables to the number of quarters and dimes.
Let's say the number of quarters is "q" and the number of dimes is "d".
We know that the total number of coins in the bag is 15, so we can write the equation: q + d = 15. (equation 1)
We also know that the total value of the coins is $2.70. Since the value of each quarter is $0.25 and the value of each dime is $0.10, we can write the equation: (0.25 * q) + (0.10 * d) = 2.70. (equation 2)
Now, we can solve this system of equations using substitution.
From equation 1, we can solve for q: q = 15 - d.
We can substitute this value of q in equation 2, so we have (0.25 * (15 - d)) + (0.10 * d) = 2.70.
Simplifying this equation gives us: 3.75 - 0.25d + 0.10d = 2.70.
Now, we can combine like terms: -0.15d = 2.70 - 3.75.
Simplifying further, we get: -0.15d = -1.05.
Dividing both sides by -0.15, we find: d = 7.
Now, substituting this value of d back into equation 1: q + 7 = 15.
Subtracting 7 from both sides, we find: q = 8.
Therefore, there are 8 quarters and 7 dimes in the bag.