Question

If 30 lb of rice and 20 lb of potatoes cost ​$18.20​, and 20 lb of rice and 12 lb of potatoes cost ​$11.52​, how much will 10 lb of rice and 50 lb of potatoes​ cost? let x be the cost of 1 lb of rice and y be the cost of 1 lb of potatoes. set up two linear equations from the given information using x and y as the variables.

Answer 1

⇒let the cost of 1 Ib of rice be "x" and that of 1 ib of potatoes be "y" 
               
         30x + 20y = 18.20..........equation ( i )
          20x + 12y =11.52...........equation ( ii )

⇒30x + 20y = 18.20.........×2
⇒20x + 12y = 11.52.........×3

          60x + 40y = 36.40
          60x + 36y = 34.56
                  ↓
            4y = 1.84
              y = 0.46

value of x.
30x = 18.20 - 20(0.46)
 30x = 9
    x = 0.3

 cost of 10 ib of rice and 50 ib of potatoes?
      10x + 50y = ?
      10(0.3) + 50(0.46) = 26

Answer = 26 Dollars

Answer 2

You can use system of linear equations and solve them to obtain price of 1 pound of rice and 1 pound  of potato. Then you can evaluate the needed cost.

The cost of 10 lb rice and 50 lb potatoes is $26

What is a system of linear equation and how to solve it?

We consider system of linear equations in two variables.

Let they be

$a_1x + b_1y = c_1\\a_2x + b_2y = c_2$

Then we can use methods like substitution or evaluation and other methods to solve those equations(solving the system of linear equations means finding the values of unknown variables for which those equations satisfy). Sometimes there is 1 solution, or infinite or no solutions.

How to use linear equations to find the needed cost in the given context?

Since the price of 1 lb of rice is x

and the price of 1 lb potatoes is y,

thus, by given conditions, we have:

30 lb of rice and 20 lb of potatoes cost ​$18.20

and 20 lb of rice and 12 lb of potatoes cost ​$11.52

or

$30 \times x + 20 \times y = \ 18.2\\20 \times x + 12 \times y = \ 11.52\\\\or\\\\30x + 20y = 18.2\\20x + 12y = 11.52$

We will use method of substitution.

Getting  x in terms of y in first equation:

$30x + 20y = 18.2\\30x = 18.2 -20y\\\\x = \dfrac{18.2 - 20y}{30}$

Substituting this value of x in second equation:

$20x + 12y = 11.52\\20(\dfrac{18.2 - 20y}{30}) + 12y = 11.52\\\\36.4 - 40y + 36y = 34.56\\36.4 - 34.56 = 4y\\y = \dfrac{1.84}{4} = 0.46$

Substituting this value of y in the equation obtained for variable x:

$x = \dfrac{18.2 - 20y}{30}\\\\x = \dfrac{18.2 - 20 \times 0.46}{30}\\\\x = \dfrac{18.2 - 9.2}{30}\\\\x = \dfrac{9}{30} = 0.3$

Thus, price of 1 lb of rice = x = $0.3

price of 1 lb of potatoes = y = $0.3

Finding cost of 10 lb rice and 50 lb potatoes:

$\text{cost of 1 lb of rice and y be the cost of 1 lb of potatoes} = 10x + 50y\\\text{Cost} = 10 \times 0.3 + 50 \times 0.46 = 3 + 23 = \ 26$

Thus, the cost of 1 lb of rice and y be the cost of 1 lb of potatoes will be $26

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