Aiden has $\$200$ with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get $40$ hats. If Aiden purchases only t-shirts, he will get $80$ t-shirts. Which of the following best models the relationship between the number of hats, $h$ , and the number of t-shirts, $t$ , that Aiden could purchase with this money? $\newline$ Choose $1$ answer: $\newline$ (A) $40h+80t=400$ $\newline$ (B) $80h+40t=200$ $\newline$ (C) $5h+2.5t=200$ $\newline$ (D) $2.5h+5t=200$

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Solve one-step and two-step equations: word problems

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Q. Aiden has

\$200

with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get

40

hats. If Aiden purchases only t-shirts, he will get

80

t-shirts. Which of the following best models the relationship between the number of hats,

h

, and the number of t-shirts,

t

, that Aiden could purchase with this money?

\newline

Choose

1

answer:

\newline

(A)

40h+80t=400

\newline

(B)

80h+40t=200

\newline

(C)

5h+2.5t=200

\newline

(D)

2.5h+5t=200

Calculate Hat Cost: Let's determine the cost of one hat. If Aiden can buy $40$ hats with $\$200$ , then the cost of one hat is $\$200$ divided by $40$ hats. $\newline$ $\$200 / 40$ hats = $\$5$ per hat.
Calculate T-shirt Cost: Now, let's determine the cost of one t-shirt. If Aiden can buy $80$ t-shirts with $\$200$ , then the cost of one t-shirt is $\$200$ divided by $80$ t-shirts. $\newline$ $\$200 / 80$ t-shirts = $\$2.50$ per t-shirt.
Create Cost Equation: We need to find an equation that models the relationship between the number of hats, $h$ , and the number of t-shirts, $t$ , that Aiden could purchase with $\$200$ . Since each hat costs $\$5$ and each t-shirt costs $\$2.50$ , the total cost when Aiden buys $h$ hats and $t$ t-shirts would be $5h + 2.5t$ .
Total Cost Equation: The total amount Aiden can spend is \$$200$, so the equation that represents the total cost of $h$ hats and $t$ t-shirts is:$\newline$$5h + 2.5t = \$200$.
Match with Options: Now, let's match our equation with the given options. The correct equation is $5h + 2.5t = 200$, which corresponds to option $(C)$.