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Learning Task 4
Solve the problem involving systems of linear equations in two variables.
1. Your mother bought 20 kilos of mangoes and atis combined. Mango is Php 60.00 per kilo and atis is Php 40.00 per kilo. If she paid Php 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 atis, then the equation is:
(b) Equation for the Cost of the fruits:
(c) The system of equations are:
(d) Solve by any method
(e) Check if your result will satisfy the problem.

Sagot :

BiegeREBORNgo

Answer:

x = 10 and y = 10

Step-by-step explanation:

SOLUTION:

(a)

Let:

x = number of kilos of mango

y = number of kilos of atis

The sum of number of kilos of mango and number of kilos of atis is equivalent to the total kilos of fruits. Since the total is 20, the equation is:

x + y = 20 (ANSWER)

(b)

The cost is equal to price per kilo multiplied by the number of kilos for each fruit.

Cost of mango = price per kilo of mango x number of kilos of mango

Cost of mango = (60 pesos/kilo)(x kilos)

Cost of mango = 60x pesos

Cost of atis = price per kilo of atis x number of kilos of atis

Cost of atis = (40 pesos/kilo)(y kilos)

Cost of atis = 40y pesos

The cost of the fruits is equal to the sum of the cost of mango and the cost of atis. Since the total cost is 1000 pesos, the equation of the cost of fruits is:

60x + 40y = 1000 (ANSWER)

(c)

Let's say the total kilos of fruits is equation 1 and the total cost of the fruits is equation 2:

x + y = 20 (Equation 1)                  (ANSWER)    

60x + 40y = 1000 (Equation 2)    (ANSWER)

(d)

Solving for x and y using substitution method:

In equation 1, isolate x

x + y = 20

x = 20 - y (Equation 3)

Substitute equation 3 in equation 2

60x + 40y = 1000

60(20 - y) + 40y = 1000

Simplify and solve for y

60(20) - 60(y) + 40y = 1000

1200 - 60y + 40y = 1000

1200 - 20y = 1000

-20y = 1000 - 1200

-20y = 200

[tex]\mathsf{y=\dfrac{-200}{-20}}[/tex]

y = 10 (ANSWER)

Substitute the value of y in equation 3

x = 20 - y

x = 20 - 10

x = 10 (ANSWER)

(e)

In equation 1:

x + y = 20

10 + 10 = 20

20 = 20 (okay)

In equation 2:

60x + 40y = 1000

60(10) + 40(10) = 1000

600 + 400 = 1000

1000 = 1000 (okay)

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