Fatima plans to spend at least $15 and at most $20 on sketch pads and pencils. If she buys 2 sketch pads, how many pencils can she buy while staying in her price range?
Fatima can buy between and pencils.
(Type whole numbers. Use ascending order.)
To find out how many pencils Fatima can buy, we need to subtract the cost of two sketch pads (which is not specified in the given range) from the maximum amount she plans to spend (which is $20).
Let's assume the cost of two sketch pads is $x.
Therefore, Fatima can spend a maximum of $20 - $x on pencils.
Since Fatima plans to spend at least $15, we can write the following inequality:
$15 ≤ $20 - $x
To isolate x, we subtract $20 on both sides:
$15 - $20 ≤ - $x
Therefore, - $5 ≤ - $x
By multiplying both sides by -1 (and flipping the inequality sign):
$5 ≥ $x
So, $5 is the maximum cost for two sketch pads.
Now, to determine how many pencils Fatima can buy with the remaining amount, we subtract the minimum cost of two sketch pads ($15) from the maximum Fatima plans to spend ($20):
$20 - $15 = $5
Therefore, Fatima can buy at least $5 worth of pencils.
If the price of a single pencil is p dollars, then the maximum number of pencils Fatima can buy is calculated by dividing the maximum amount she can spend on pencils ($5) by the price of a single pencil.
Therefore, the maximum number of pencils Fatima can buy is $5/p.
However, since we are looking for a whole number answer, we need to consider the scenario where Fatima spends the most on pencils (when p = 1), as well as the scenario where she spends the least on pencils (when p = 5).
Therefore, Fatima can buy between 5 and 1 pencils while staying in her price range.