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ALGEBRA 1 HELP!! Andrea buys 4 bags of granola and 3 bags of dried fruit. She spends $51.50. Carter buys 2 bags of granola and 4 bags of dried fruit and spends $45.50
Write and solve a system of equations to determine the cost of a bag of granola and the cost of a bag of fruit.

Sagot :

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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  One bag of dried fruit is $7.90.

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   One bag of granola is $6.95

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Check to see if these values work:

Andrea:

4G + 3F = $51.50  :

4($6.95) + 3($7.90) = $51.50  ?

$51.50 = $51.50   YES

Carter:

2G + 4F = $45.50

2($6.95) + 4($7.90) = $45.50  ?

$45.50                     =  $45.50   YES

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