Question 1184549: Angel budgets from USD300 to USD600 for trees and shrubs to landscape their yard. The available money he has now are in dollars. After shopping around, he finds that good trees cost USD150 and mature shrubs cost USD75. What combinations of trees and shrubs can he afford to buy?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The cost of a tree, $150, is twice the cost of a shrub, $75. That means the total cost of any number of trees and shrubs will be a multiple of $75.
The budget amount can be anywhere from $300 to $600. The multiples of $75 from $300 to $600 are $300, $375, $450, $525, and $600.
The total cost will be a multiple of $10 only if the number of shrubs is even.
So look at each possible total cost and determine the number of possible combinations for that total.
(1) $300
$300 is a multiple of $10, so the number of shrubs is even.
The maximum number of shrubs is $300/$75 = 4.
The number of shrubs can be 0, 2, or 4.
3 possible combinations -- 0 shrubs and 2 trees, 2 shrubs and 1 tree, and 4 shrubs and 0 trees.
(2) $375
$375 is not a multiple of $10, so the number of shrubs is odd.
The maximum number of shrubs is $375/$75=5.
The number of shrubs can be 1, 3, or 5.
3 possible combinations -- 1 shrub and 2 trees, 3 shrubs and 1 tree, and 5 shrubs and 0 trees.
Do the same analysis for totals of $450, $525, and $600 to finish finding the different possible combinations.
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