Question

Solve the problem involving systems of lineas equations

1. Your mother bought 20 kilos of mangoes and apple combined. Mango P60.00 per kilo and apple is P40.00 per kilo. If she paid P 1000.00 for 20 kilos how many kilos of each kind mother bought?

(a) If x is number of kilos of mango and number of kilos of apple, then the equation is:______

(b) Equation for the cost of fruits_______

(c) The system equations are ______ and _________

(d) Solve by any method.

(e) Check if your result will satisfy the problem.​​

Answer 1

x = 10

y = 10

Explanation:

60x + 40y = 1000

x + y = 20

a. If x is number of kilos of mango and number of kilos of apple, then the equation is: x + y = 20

b. Equation for the cost of fruits

60x + 40y = 1000

c. The system equations are x + y = 20 and 60x + 40y = 1000

d. Solve by any method.

60x + 40y = 1000 (2)

x + y = 20 (1)

x = 20 - y

Substitute into (2)

60x + 40y = 1000 (2)

60(20 - y) + 40y = 1000

1200 - 60y + 40y = 1000

- 20y = 1000 - 1200

-20y = - 200

y = -200/-20

= 10

y = 10

Substitute y = 10 into (1)

x + y = 20

x + 10 = 20

x = 20 - 10

x = 10

(e) Check if your result will satisfy the problem.​​

60x + 40y = 1000

60(10) + 40(10) = 1000

600 + 400 = 1000

1000 = 1000