Question

Jada is throwing a graduation party for her sister. Three tablecloths and 15 centerpieces cost $30. Later, she bought 4 centerpieces and 2 tablecloths for $11. How much is one tablecloth?d

Answer 1

Let's say that the price of one tablecloth is "x" and the price of one centerpiece is "y", we know that

$3x+15y=30$

Also

$2x+4y=11$

Then we must solve a system of equations

$\begin{cases}3x+15y=30{} \\ 2x+4y={11}\end{cases}$

We have multiple ways to solve that system of equations, we just want to find the value of "x", then, let's do a substituition method to solve it for x.

$y=\frac{30-3x}{15}$

Then

$\begin{gathered} 2x+4y=11 \\ \\ 2x+4\cdot\frac{30-3x}{15}=11 \\ \\ 2x+\frac{120-12x}{15}=11 \\ \\ 2x+\frac{120}{15}-\frac{12x}{15}=11 \\ \\ 2x-\frac{12x}{15}=11-\frac{120}{15} \\ \\ \frac{30x}{15}-\frac{12x}{15}=\frac{165}{15}-\frac{120}{15} \\ \\ 30x-12x=165-120 \\ \\ 18x=45 \\ \\ x=\frac{45}{18}=2.5 \end{gathered}$

The price of one tablecloth is $2.5