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QuestionLaTanya buys 5 yards of blue and 8 yards of green fabric for \$62. Blue costs \$2 more per yard. Find the combined cost of 1 yard of each.

Studdy Solution

STEP 1

Assumptions1. Laanya buys5 yards of blue fabric. She also buys8 yards of green fabric3. The blue fabric costs moreperyardthanthegreenfabric4.Thetotalcostofallthefabricis more per yard than the green fabric4. The total cost of all the fabric is 62

STEP 2

Let's denote the cost of the green fabric per yard as xx. Then, the cost of the blue fabric per yard would be x+2x +2.

STEP 3

We can set up an equation to represent the total cost of the fabric. The total cost is the sum of the cost of the blue fabric and the cost of the green fabric.
Total cost=Cost of blue fabric+Cost of green fabricTotal\, cost = Cost\, of\, blue\, fabric + Cost\, of\, green\, fabric

STEP 4

Substitute the quantities and prices into the equation.
$62=(x+2)+8x\$62 =(x +2) +8x

STEP 5

implify the equation by distributing the5 to the terms inside the parentheses.
$62=5x+10+8x\$62 =5x +10 +8x

STEP 6

Combine like terms.
$62=13x+10\$62 =13x +10

STEP 7

Subtract10 from both sides of the equation to isolate the term with xx.
$52=13x\$52 =13x

STEP 8

Divide both sides of the equation by13 to solve for xx.
x=$52/13x = \$52 /13

STEP 9

Calculate the value of xx.
x=$4x = \$4

STEP 10

Now that we have the cost of the green fabric, we can find the cost of the blue fabric by adding $2 to the cost of the green fabric.
Cost of blue fabric=x+2Cost\, of\, blue\, fabric = x +2

STEP 11

Substitute the value of xx into the equation.
Cost of blue fabric=$4+Cost\, of\, blue\, fabric = \$4 +

STEP 12

Calculate the cost of the blue fabric.
Cost of blue fabric=$6Cost\, of\, blue\, fabric = \$6

STEP 13

The combined cost of yard of blue fabric and yard of green fabric is the sum of the cost of the blue fabric and the cost of the green fabric.
Combined cost=Cost of blue fabric+Cost of green fabricCombined\, cost = Cost\, of\, blue\, fabric + Cost\, of\, green\, fabric

STEP 14

Substitute the values into the equation.
Combined cost=$6+$4Combined\, cost = \$6 + \$4

STEP 15

Calculate the combined cost.
Combined cost=$10Combined\, cost = \$10The combined cost of yard of blue fabric and yard of green fabric is $10.

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