Question

1. Se tiene que 5 kilogramos (kg) de almendra y 4 kg de nuez cuestan $44.00, mientras que 8 kg de almendra y 6 kg de nuez cuestan $69.00. Encuentra el precio por kilogramo de cada producto.

Answer 1

x = 6.00 $/kg ----> almond

y = 3.5 $/kg ------> nut

Explanation:

To find the price per kg of each product you first write the algebraic equations for the given relations:

x : price per kg of almond

y: price per kg of nut

Then, you have:

5x + 4y = 44.00 (1)

8x + 6y = 69.00 (2)

By using substitution you have from (1):

y = (44.00-5x)/(4) = 11.00 - (5/4)x

you replace this expression for y into (2):

8x+6[11.00-(5/4)x] = 69.00

8x+66.00-(15/2)x = 69.00

8x-(15/2)x = 69.00 - 66.00

(1/2)x = 3.00

x = 6.00 $/kg ----> almond

And for nut:

y = 11.00 - (5/4)x = 11.00 - (5/4)(6.00) = 3.5$/kg

y = 3.5 $/kg ------> nut