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one day a store sold 12 sweatshirts white one cost $9.95 and yellow ones cost $12.50. In all 147.45 worth of sweatshirts were sold how many of each color were sold?

Respuesta :

Americ
x= # of white sweatshirts
y= # of yellow sweatshirts

STEP 1:
set up quantity and cost equations

QUANTITY EQUATION
x + y= 12

COST EQUATION
$9.95x + $12.50y= $147.45


STEP 2:
solve for one variable in quantity equation

x + y= 12
subtract y from both sides

x= 12 - y


STEP 3:
substitute x value in step 2 in cost equation

$9.95x + $12.50y= $147.45
9.95(12 - y) + 12.50y= 147.45

multiply 9.95 by parentheses
(9.95*12) + (9.95*-y) + 12.50y= 147.45

119.40 - 9.95y + 12.50y= 147.45
combine like terms

119.40 + 2.55y= 147.45
subtract 119.40 from both sides

2.55y= 28.05
divide both sides by 2.55

y= 11 yellow


STEP 4:
substitute step 3 x value in either equation

x + y= 12
x + 11= 12
x= 1 white


CHECK:
$9.95x + $12.50y= $147.45
9.95(1) + 12.50(11)= 147.45
9.95 + 137.50= 147.45
147.45= 147.45


ANSWER: 1 white sweatshirt and 11 yellow sweatshirts were sold.

Hope this helps! :)

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