High School

Solve the problem involving systems of linear equations:

1. Your mother bought 20 kilos of mangoes and apples combined. Mangoes cost P60.00 per kilo, and apples cost P40.00 per kilo. If she paid P1000.00 for 20 kilos, how many kilos of each kind did your mother buy?

(a) If \( x \) is the number of kilos of mangoes and \( y \) is the number of kilos of apples, then the equation is:
\[ x + y = 20 \]

(b) Equation for the cost of fruits:
\[ 60x + 40y = 1000 \]

(c) The system of equations is:
\[ x + y = 20 \]
\[ 60x + 40y = 1000 \]

(d) Solve the system by any method.

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

Answer :

Answer:

x = 10

y = 10

Step-by-step 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

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