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

Question

Write and solve a system of equations to determine the cost of a bag of granola and the cost of a bag of fruit.

Answer 1

Let g be the cost of a bag of granola and f be the cost of a bag of fruit.

Andrea's purchase: 4g + 3f = 51.50. Call this equation (1).

Carter's purchase: 2g + 4f = 45.50. Call this equation (2)

Multiply (2) by -2 and get: -4g - 8f = -91. Call this equation (3).

Now add (1) and (3) and get: -5f = -39.50. Solve for f and get: f = 7.90.

Now, plug in the value of f into (1) (or (2), you'll get the same result) and get:

4g + 3(7.90) = 51.50

4g = 51.50 - 23.7

4g = 27.8

g = 6.95.

Therefore one bag of granola costs $6.95 and one bag of fried fruit costs $7.90.