Brent has #3.35 in quarters and dimes. He has 23 coins in all. How many quarters and dimes does he have? Write a system of equations to solve
there are 16 dimes and 7 quarters
There are 16 dimes and 7 quarters
Sure, here's a system of equations to solve the problem:
Let's assume that Brent has x number of quarters and y number of dimes.
1. The total value of quarters is $0.25 * x.
2. The total value of dimes is $0.10 * y.
3. The total value of quarters and dimes is $3.35, so we have the equation: $0.25 * x + $0.10 * y = $3.35.
4. Brent has a total of 23 coins, so we have another equation: x + y = 23.
Now you can solve this system of equations to find the values of x and y. Good luck!
To answer this question, we can set up a system of equations based on the given information.
Let's assume that Brent has x quarters and y dimes.
The first equation can be derived from the total value of the coins, which is $3.35. We know that the value of each quarter is $0.25, and the value of each dime is $0.10. So, the equation becomes:
0.25x + 0.10y = 3.35 ---- (equation 1)
The second equation comes from the total number of coins, which is 23. Since Brent has x quarters and y dimes, the equation becomes:
x + y = 23 ---- (equation 2)
Now we have a system of equations:
0.25x + 0.10y = 3.35
x + y = 23
We can solve this system of equations to find the values of x and y, representing the number of quarters and dimes Brent has.
There are several methods to solve a system of equations, including substitution, elimination, or graphing. Let's solve it using the substitution method for this particular example:
From equation 2, we can isolate x by subtracting y on both sides:
x = 23 - y
Now we substitute this value of x into equation 1:
0.25(23 - y) + 0.10y = 3.35
Distribute the 0.25 across the parentheses:
5.75 - 0.25y + 0.10y = 3.35
Combine like terms:
-0.15y = 3.35 - 5.75
-0.15y = -2.40
Divide both sides by -0.15 to solve for y:
y = -2.40 / -0.15
y = 16
Now substitute the value of y back into equation 2 to solve for x:
x + 16 = 23
x = 23 - 16
x = 7
Therefore, Brent has 7 quarters and 16 dimes.
d+q = 23
10d+25q = 335