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=(30-3x)/(15)`

Then

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

The price of one tablecloth is $2.5