a clipboard costs $2.23. It costs $0.58 more than a notebooh. Lisa buys two clipboards and one notebook and paid with a ten dollar bill. use a tape diagram with calculations to show her change.
Don't understand tape diagrams
3.84
Need help with it all
To solve this problem using a tape diagram and calculations, we'll follow these steps:
Step 1: Understand the problem:
Lisa buys two clipboards and one notebook, and the total cost of the items is $10. We also know that a clipboard costs $0.58 more than a notebook.
Step 2: Assign variables:
Let's assign variables to the unknowns to help us create the tape diagram and solve the problem more easily. Let's use:
C = cost of a clipboard
N = cost of a notebook
Step 3: Set up the equation:
We are told that a clipboard costs $0.58 more than a notebook, so we can set up the equation:
C = N + $0.58
Step 4: Create the tape diagram:
We'll represent the total cost of the two clipboards and one notebook using a tape diagram. Let's use rectangles to represent the costs.
Cost of two clipboards = 2C
Cost of one notebook = N
Therefore, the equation for the tape diagram is:
2C + 1N = $10
Step 5: Solve the equation:
We'll substitute the value of C using the equation from step 3 to replace C in the tape diagram equation:
2(N + $0.58) + N = $10
Distribute:
2N + $1.16 + N = $10
Combine like terms:
3N + $1.16 = $10
Subtract $1.16 from both sides:
3N = $10 - $1.16
3N = $8.84
Divide both sides by 3:
N = $8.84 / 3
N ≈ $2.95
So the cost of one notebook is approximately $2.95.
Step 6: Find the cost of a clipboard:
To find the cost of a clipboard, substitute the value of N into the equation from step 3:
C = $2.95 + $0.58
C ≈ $3.53
So the cost of one clipboard is approximately $3.53.
Step 7: Calculate Lisa's change:
To find Lisa's change, subtract the total cost of the items from the amount she paid:
Total cost = (2C) + N = (2 * $3.53) + $2.95 = $7.06 + $2.95 = $10.01
Change = Amount Paid - Total Cost = $10 - $10.01 = -$0.01
Lisa doesn't receive any change since she paid exactly the amount needed.
In conclusion, Lisa's change is -$0.01, which means she did not receive any change.