Tina's change of $1.35 consisted of quarters and dimes only and she received twice as many dimes as quarters. How many dimes were there?
Let x = quarters
Let 2x = dimes
Equation:
.25(x) + .10(2x) = 1.35
Solve for x. Remember to determine the number of dimes for your answer.
Why did the math book look sad? Because it had too many problems!
Now, let's solve the math problem! Let's say the number of quarters Tina had is q. Since Tina had twice as many dimes as quarters, she had 2q dimes.
The value of quarters can be calculated as 0.25q and the value of dimes can be calculated as 0.10(2q). The total value of all coins is $1.35, so we can write the equation:
0.25q + 0.10(2q) = 1.35
Let's simplify it:
0.25q + 0.20q = 1.35
Combining the like terms gives:
0.45q = 1.35
Now, divide both sides by 0.45 to solve for q:
q = 1.35 / 0.45
q = 3
Therefore, Tina had 3 quarters. Since she had twice as many dimes, she had 2 * 3 = 6 dimes. So, there were 6 dimes in total.
Let's solve this step-by-step.
Step 1: Assign variables
Let's say the number of quarters is q, and the number of dimes is d.
Step 2: Set up equations
We know that Tina's change consists of quarters and dimes only, and the total value of the change is $1.35.
The value of quarters is 0.25 * q.
The value of dimes is 0.10 * d.
We can write the equation as:
0.25 * q + 0.10 * d = 1.35
We also know that Tina received twice as many dimes as quarters, so we can write another equation:
d = 2q
Step 3: Solve the equations
Substitute the value of d from the second equation into the first equation:
0.25 * q + 0.10 * (2q) = 1.35
Simplify the equation:
0.25q + 0.20q = 1.35
0.45q = 1.35
Divide both sides of the equation by 0.45:
q = 1.35 / 0.45
q = 3
So the number of quarters is 3.
Now, substitute the value of q into the second equation to find the value of d:
d = 2 * q
d = 2 * 3
d = 6
So the number of dimes is 6.
Step 4: Answer the question
There were 6 dimes.
To solve this problem, let's break it down step by step:
Step 1: Assign variables
Let's assign variables to the quantities we need to find. Let Q represent the number of quarters and D represent the number of dimes.
Step 2: Set up equations
We know that Tina's change consists of quarters and dimes only. The value of a quarter is $0.25, so the total value of quarters can be represented as 0.25Q. Similarly, the value of a dime is $0.10, so the total value of dimes can be represented as 0.10D.
The total value of the change is $1.35, so we can set up the equation:
0.25Q + 0.10D = 1.35
We also know that Tina received twice as many dimes as quarters, so we can set up another equation:
D = 2Q
Step 3: Solve the equations
Substitute the second equation into the first equation to eliminate the variable D:
0.25Q + 0.10(2Q) = 1.35
Simplify and solve for Q:
0.25Q + 0.20Q = 1.35
0.45Q = 1.35
Q = 1.35 / 0.45
Q = 3
Now that we know the number of quarters (Q = 3), we can find the number of dimes using the second equation:
D = 2Q
D = 2 * 3
D = 6
Therefore, there were 6 dimes in Tina's change.