To determine the correct expression for the total cost of fabric Aiko needs, let's break down the situation:
- The cost of fabric is $7.99 per yard.
- Aiko requires 213 yards of solid color fabric.
- The expression should represent the total cost, which includes both the solid color fabric and the patterned fabric.
We can denote the amount of patterned fabric in yards as \( x \).
Therefore, the total yards of fabric Aiko needs will be:
- Solid fabric: 213 yards
- Patterned fabric: \( x \) yards
The total number of yards of fabric Aiko is purchasing would then be \( 213 + x \) yards.
Since the cost per yard is $7.99, the total cost can be expressed as: \[ \text{Total Cost} = \text{Cost per yard} \times \text{Total yards} = 7.99 \times (213 + x) \]
This can be simplified to: \[ \text{Total Cost} = 7.99 \times 213 + 7.99 \times x \]
However, we need to express it in a way that fits one of the given answer choices.
We can see the cost of the solid fabric alone is: \[ 7.99 \times 213 \]
And then add \( 7.99x \) for the patterned fabric.
Now looking at the options:
A) \( 18.64 + 7.99x \) (Incorrect) B) \( 18.64x + 7.99 \) (Incorrect) C) \( 7.99x + 213 \) (Incorrect) D) \( 213x + 7.99 \) (Incorrect)
None of the options accurately represent the total cost expression derived from our analysis:
The correct expression should have been in the form: \[ 7.99 \times (213 + x) \] which is not listed.
If forced to choose one option, option C, \( 7.99x + 213 \), would not correctly calculate the total cost since it misrepresents the dollar amount for yards of solid fabric and does not multiply by the cost per yard.
With the information provided, it seems like there is no correct answer option in this selection matching the total cost calculation.
1 answer