You have $2.75 in dimes and quarters, and you have a total of 17 dimes and quarters. How many of each type of coin do you have?
D+Q=17
or Q=17-D
and 10D+25Q=275
or 10D+25(17-D)=275
solve for D, then solve for Q
Distribute 25
10D+425-25D=275
Add like variables
425-15D=275
Subtract 425
-15D=-150
Divide Each Side by -15
D=10
Plug D into equation to solve for Q.
Q=17-10
Q=7
To determine the number of dimes and quarters you have, let's set up a system of equations based on the given information.
Let's say "d" represents the number of dimes and "q" represents the number of quarters.
From the information given, we can form the following two equations:
1) The total value of dimes and quarters is $2.75: 0.10d + 0.25q = 2.75 (since a dime is $0.10 and a quarter is $0.25)
2) The total number of dimes and quarters is 17: d + q = 17
Now we have a system of two equations with two variables. We can solve this system to find the values of "d" and "q".
There are multiple methods to solve this system, one of which is substitution. To use substitution, we will solve one equation for one variable and substitute that expression into the other equation.
Let's solve equation 2 for "d":
d = 17 - q
Now substitute this expression for "d" in equation 1:
0.10(17 - q) + 0.25q = 2.75
Simplify the equation:
1.70 - 0.10q + 0.25q = 2.75
Combine like terms:
0.15q = 2.75 - 1.70
0.15q = 1.05
Divide both sides by 0.15:
q = 1.05 / 0.15
q = 7
Now that we have the value of "q", we can substitute it back into equation 2 to find the value of "d":
d + 7 = 17
d = 17 - 7
d = 10
Therefore, you have 10 dimes and 7 quarters.