Question

Ten granola bars and twelve bottles of water cost $23. Five granola bars and four bottles of water cost $10. How much do one granola bar and one bottle of water cost?Part BFor a fundraiser, a group plans to sell granola bars and bottles of water at the same prices as described in Part A. The group wants the income from the fundraiser to be at least $150.Choose the inequality to show the number of granola bars x and the number of bottles of water y that must be sold.

Answer 1

Let g = cost of granola bars

b = cost of a bottle of water

10g+12b = 23

5g + 4b = 10

Multiply the second equation by -2

-10g -8b = -20

Add this to the first equation

10g+12b = 23

-10g -8b = -20

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4b = 3

Divide by 4

4b/4 = 3/4

b = 3/4 or .75

Now find g

5g + 4(3/4) = 10

5g + 3 = 10

5g = 7

g = 7/5

g = 1.4

We want to find 1g+ 1b

1.4+ .75 =2.15

Part B

We want our income to be at least 150

The cost of granola bars is 1.4 and we are selling x of them

The cost of water is .75 and we are selling y of them

It must be at least >=

1.4x + .75y >= 150