Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

The girls’ volleyball team is selling T-shirts and pennants to raise money for new uniforms. The team hopes to raise more than \(250.

Item	Price
T-shirt	\)10
Pennant	$4

Which of the following combinations of items sold would meet this goal?

F 16 T-shirts and 20 pennants

G 20 T-shirts and 12 pennants

H 18 T-shirts and 18 pennants

J 15 T-shirts and 25 pennants

Short answer

The combination of items sold that would meet this goal is 18 T-shirts and 18 pennants.

Therefore, the option His correct.

Step-by-step solution

Step 1. Write the inequality for the given problem.

It is given that the price of 1 T-shirt is $10 and price of 1 pennant is $4.

Let $x$and $b$be the number of T-shirts and pennants respectively.

The price of 1 T-shirt is $10. Therefore, the price of$x$ T-shirts is .

The price of 1 pennant is $4. Therefore, the price of$y$ pennants is .

The total price of T-shirts $x$and $y$pennants is $\$\left(10x+4y\right)$.

The sum of the money is more than $250.

Therefore, the inequality for the given problem is:

$\begin{array}{c}10x+4y>250\\ 2\left(5x+2y\right)>250\\ \frac{2\left(5x+2y\right)}{2}>\frac{250}{2}\\ 5x+2y>125\end{array}$

Step 2. Determine the combination of items sold that would meet this goal.

The inequality for the given problem is:

$5x+2y>125$

If the number of T-shirts is 16 and the number of pennants is 20, that implies if the value of is 16 and the value of is 20 then it can be observed that:

$\begin{array}{c}5x+2y>125\\ 5\left(16\right)+2\left(20\right)>125\\ 80+40>125\\ 120>125\end{array}$

The condition obtained is$120>125$which is false, Therefore, the values $x=16$and$y=20$does not satisfy the inequality $5x+2y>125$.

If the number of T-shirts is 20 and the number of pennants is 12, that implies if the value of$x$is 20 and the value of$y$is 12 then it can be observed that:

$\begin{array}{c}5x+2y>125\\ 5\left(20\right)+2\left(12\right)>125\\ 100+24>125\\ 124>125\end{array}$

The condition obtained is $124>125$which is false, Therefore, the values $x=20$and $y=12$does not satisfy the inequality $5x+2y>125$.

If the number of T-shirts is 18 and the number of pennants is 18, that implies if the value of$x$is 18 and the value of$y$is 18 then it can be observed that:

$\begin{array}{c}5x+2y>125\\ 5\left(18\right)+2\left(18\right)>125\\ 90+36>125\\ 126>125\end{array}$

The condition obtained is$126>125$which is true, Therefore, the values$x=18$and$y=18$satisfies the inequality $5x+2y>125$.

If the number of T-shirts is 15 and the number of pennants is 25, that implies if the value of $x$is 15 and the value of $y$is 25 then it can be observed that:

$\begin{array}{c}5x+2y>125\\ 5\left(15\right)+2\left(25\right)>125\\ 75+50>125\\ 125>125\end{array}$

The condition obtained is$125>125$ which is false, Therefore, the values$x=15$ and$y=25$ does not satisfy the inequality $5x+2y>125$.

As, the values$x=18$ and$y=18$ satisfies the inequality $5x+2y>125$. Therefore, $x=18$and$y=18$ are the solutions of the inequality $5x+2y>125$.

Therefore, the combination of items sold that would meet this goal is 18 T-shirts and 18 pennants.

Therefore, the option H is correct.