Question

At a lunch stand, each hamburger has $50$ more calories than each order of fries. If $2$ hamburgers and $3$ orders of fries have a total of $1700$ calories, how many calories does a hamburger have?

Answer 1

Finding the calories of a hamburger:

Given that each hamburger has $50$ more calories than each order of fries.

$2$ hamburgers and $3$ orders of fries have a total of $1700$ calories.

Let, $h$ be the calories of in a hamburger and $f$ be the calories in an order of fries.

Then,

$$\begin{gathered} h=f+50...\left(1\right) \\ 2h+3f=1700...\left(2\right) \end{gathered}$$

Substituting $\left(1\right)$ in $\left(2\right)$, we get

$$\begin{gathered} \therefore 2(f+50)+3f=1700 \\ \Rightarrow 2f+100+3f=1700 \\ \Rightarrow 5f=1600 \\ \Rightarrow f=320 \end{gathered}$$

Substituting $f=320$ in $\left(1\right)$, we get

$$\begin{gathered} \therefore h=f+50 \\ \Rightarrow h=320+50 \\ \Rightarrow h=370 \end{gathered}$$

Hence, the hamburger has $370$ calories.