The problem provides a table showing the amount of onion and meat needed for one serving of hamburger and stew. Hamburger requires 20g of onion and 80g of meat per serving. Stew requires 30g of onion and 50g of meat per serving. A certain amount of hamburger and stew were made. A total of 210g of onion and 490g of meat were used. Let $x$ be the number of servings of hamburger and $y$ be the number of servings of stew. The problem asks us to create a system of equations and solve for $x$ and $y$.

1. Problem Description

The problem provides a table showing the amount of onion and meat needed for one serving of hamburger and stew.

Hamburger requires 20g of onion and 80g of meat per serving.

Stew requires 30g of onion and 50g of meat per serving.

A certain amount of hamburger and stew were made. A total of 210g of onion and 490g of meat were used.

Let $x$ be the number of servings of hamburger and $y$ be the number of servings of stew.

The problem asks us to create a system of equations and solve for $x$ and $y$.

2. Solution Steps

First, we create an equation for the amount of onion used. The total amount of onion used is the sum of the onion used for hamburger and the onion used for stew, which is 210g.

$20x + 30y = 210$

Next, we create an equation for the amount of meat used. The total amount of meat used is the sum of the meat used for hamburger and the meat used for stew, which is 490g.

$80x + 50y = 490$

Now we have a system of two equations with two variables:

$20x + 30y = 210$

$80x + 50y = 490$

We can simplify the first equation by dividing both sides by 10:

$2x + 3y = 21$

We can simplify the second equation by dividing both sides by 10:

$8x + 5y = 49$

Now we have:

$2x + 3y = 21$

$8x + 5y = 49$

We can solve this system of equations using substitution or elimination. Let's use elimination.

Multiply the first equation by -4:

$-8x - 12y = -84$

Add this to the second equation:

$(-8x - 12y) + (8x + 5y) = -84 + 49$

$-7y = -35$

$y = 5$

Now substitute $y = 5$ into the equation $2x + 3y = 21$:

$2x + 3(5) = 21$

$2x + 15 = 21$

$2x = 6$

$x = 3$

So, $x = 3$ and $y = 5$.

3. Final Answer

The number of servings of hamburger is 3 and the number of servings of stew is

5. $x = 3$ and $y = 5$.

The system of equations is:

$20x + 30y = 210$

$80x + 50y = 490$

Final Answer:

x = 3, y = 5