Your family likes to eat fruit, but because of budget constraints, you spend only $18 each week on fruit. Your two choices are apples and grapes. Apples cost $0.20 per pound, and grapes cost $0.60 per pound. Let a denote the number of pounds of apples you buy and g the number of grapes. Because of your budget, it is possible to express g as a linear function of the variable a. To find the linear formula, we need to find its slope and initial value.
(a) If you buy one more pound of apples, how much less money do you have available to spend on grapes? (Round your answer to two decimal places.)
How many fewer pounds of grapes can you buy? (Round your answer to two decimal places.)
(b) Use your answer to part (a) to find the slope of g as a linear function of a. (Hint: Remember that the slope is the change in the function that results from increasing the variable by 1. Should the slope of g be positive or negative? Round your answer to two decimal places.)
(c) To find the initial value of g, determine how many pounds of grapes you can buy if you buy no apples.
(d) Use your answer to parts (b) and (c) to find a formula for g as a linear function of a.
g = _________
a) Buying one more lb. of apples means that you have .20 less to spend on grapes, since apples are .20 lb.
Since grapes are .60 / lb. then .20 less to spend on grapes means that you will buy 20/ 60 = 1/3 lbs less or (-1/3)
b) The slope of g as it relates to a is (-1/3)/ 1 = -1/3
c) You can buy 18/.60 = 30 lbs. of grapes if you buy no apples
d) The function would be → g = (-1/3)a + 30
Check this.....if we bought 30 lbs. of apples we would spend $6 .....then...we could buy
[18 - 6] /.60 = 12/.60 = 20lbs of grapes
Plugging these into the function
20 = (-1/3)30 + 30
20 = -10 + 30
20 = 20 !!!!