Question

If 20 lb of rice and 10 lb of potatoes cost $16.20 and 30 lb of rice and 12 lb of potatoes cost $23.04, how much will 10 lb of rice and 50 lbs of potatoes cost?

Answer 1

Let x = price of rice per pound
Let y = price of potaotes per pound
20x + 10y = 16.2
30x + 12y = 23.04
Solve the system of equations for x and y.
Then substitute x and y in 10x + 50y and evaluate the expression.

Answer 2

Elimination is faster

Answer 3

The way @mathstudent55 has it is the way i need it set up.. but idk how to do elimination anyway


20x+10y=16.2 R1
30x+50y=23.04 R2

Answer 4

To use elimination you need to add the two equations and eliminate one variable. Sometimes you may have a system of equations in which for, example, one equation has 2x and the other one has -2x. Simply by adding the eqquatios, you eliminate x and you just need to solve for y. Most of the time, though, you need to multiply one equation or both by some number to be able to eliminate a variable.

Let's take this example. The first equation has 20x and the second equation has 30x. If you had -60y in the first equation and 60y in the second equation, the y's would add up to zero. In order to do that, let's multiply the entire first equation by -3 and let's multiply the entire second equation by 2. Then we'll simplify both equations and write one above the other.
(-3)(20x) + (-3)(10y) = (-3)(16.2)
-60x - 30y = -48.6

(2)(30x) + (2)(12y) = (2)(23.04)
60x + 24y = 46.08

-60x - 30y = -48.6
60x + 24y = 46.08
--------------------(add the two equations)
-6y = -2.52
Divide both sides by -6:
-6y/(-6) = -2.52/(-6)
y = 0.42

Now substitute y = 0.42 in either of the two original equations:
Let's use th efirst one
20x + 10y = 16.2
20x + 10(0.42) = 16.2
20x + 4.2 = 16.2
20x = 12
x = 0.60

Now that you know the prices per pound of rice and potatoes, use the prices in
10x + 50y to evaluate what the question asks for.