Answer:
Granola is $6.95/bag and Dried Fruit is $7.90/bag.
Step-by-step explanation:
Let G and F stand for the cost of 1 bag Granola and 1 bag dried Fruit.
We learn that Andrea's total was $51.50. Her purchase can be written as the sum of the cost of 4 bags granola (4G) and 3 bags fruit (3F):
4G + 3F = $51.50
We can do the same for Carter:
2G + 4F = $45.50
We have two equations and two unknowns, so we should be able to solve for both unknowns. To do this, we need to find a way to eliminate one of the unknows in a single equation. Let's rearrange Carter's equation to isolate G on one side:
2G + 4F = $45.50
2G = $45.50 - 4F
G = ($45.50 - 4F)/2
Now use this expression for G in Andrea's equation:
4G + 3F = $51.50
4(($45.50 - 4F)/2) + 3F = $51.50
2($45.50 - 4F) + 3F = $51.50
($91.00 - 8F) + 3F = $51.50
-5F = - $39.5
F = $7.90 <u>One bag of dried fruit is $7.90.</u>
Now use this value for F in either equation for find G:
2G = $45.50 - 4F
2G = $45.50 - 4($7.90)
2G = $13.90
G = $6.95 <u>One bag of granola is $6.95</u>
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Check to see if these values work:
<u>Andrea: </u>
4G + 3F = $51.50 :
4($6.95) + 3($7.90) = $51.50 ?
$51.50 = $51.50 <u>YES</u>
<u>Carter:</u>
2G + 4F = $45.50
2($6.95) + 4($7.90) = $45.50 ?
$45.50 = $45.50 <u>YES</u>
<u></u>
because 4>3
because 3<4