Question

EQUATIONS AND INEQUALITIESSolving a word problem with two unknowns using a line

Answer 1

225 hamburguers

Step-by-step explanation

First, we have to name the variables:

• x: number of hamburgers sold

,

• y: number of cheeseburgers sold

We know that they sold a total of 503, so one of the equations is x + y = 503.

Also, we know that the number of cheeseburgers is 53 more than the number of hamburgers, so the other equation is y = x + 53.

We have to solve the system,

`\begin{cases}x+y=503 \\ y=x+53\end{cases}`

Since we have to solve for x, we can use the substitution method. Replace y with the second equation in the first equation,

`x+(x+53)=503`

Add like terms,

`\begin{gathered} (x+x)+53=503 \\ 2x+53=503 \end{gathered}`

Subtract 53 from both sides,

`\begin{gathered} 2x+53-53=503-53 \\ 2x=450 \end{gathered}`

And divide both sides by 2,

`\begin{gathered} (2x)/(2)=(450)/(2) \\ \\ x=225 \end{gathered}`

Hence, 225 hamburgers were sold on Tuesday.