Final answer:
To determine how much candy can be bought for $12, a proportion is set up comparing the known amount of candy purchased for $9 to the unknown amount for $12. After cross-multiplication and algebraic rearrangement, it is found that one can purchase approximately 5.33 pounds of candy for $12.
Step-by-step explanation:
To solve the question, which is essentially asking how much candy one can buy for $12 given that 4 pounds cost $9, we can set up a proportion. A proportion is an equation that states that two ratios are equivalent. In this case, the ratio of the amount of candy to the price is constant.
First, recognize that the cost per pound of candy can be calculated by dividing the total cost by the weight. For the initial purchase:
$9.00 / 4 lb = $2.25 per pound
Then, set up a proportion to determine how many pounds of candy can be bought with $12:
4 lb / $9.00 = x lb / $12.00
To solve for x, cross multiply the known values and solve for the unknown variable:
4 lb * $12.00 = x lb * $9.00
Next, divide both sides of the equation by $9.00 to isolate x on one side of the equation:
4 lb * $12.00 / $9.00 = x
This simplifies to:
x = (4 lb * $12.00) / $9.00
x = $48.00 / $9.00
x = 5.33 lb
So, for $12.00, one can purchase approximately 5.33 pounds of candy, considering the same price per pound applies.