Represent the following as a linear equation, then solve.

Question

Represent the following as a system of linear equations, then solve.

 A manufacturer wishes to make 2,500 kg of a new product, which is a mixture of two different ingredients. One ingredient costs $1.4 per kg, the other in gredient costs $3.7 per kg. The new product costs a total of $2.4 per kg.

 How many kilograms of each ingredient should be used to make 2,500 kg of the new product?

Answer 1

Let the quantity of first and second ingredient in the mixture be x and y kgs respectively.

And total weight of mixture is 2500 kg.

So, x+y=2500 ---------------------(1)

Also,

The cost of x kg of first ingredient is 1.4x and cost of second ingredient in the mixture is 3.7y

And total cost of mixture is 2.4*2500 =6000

So, 1.4x+3.7y= 6000  ----------------------(2)

On multiplying (1) by 1.4 we get:

1.4x +1.4y= 3500  ---------------------(3)

On subtracting (3) from (2) we get:

2.3y = 2500

or y = 2500/2.3 or 25000/23

or y = 1086.96 kg (approx)

On putting the value of y in equation (1) we get:

x = 2500 - 25000/23

or x = 32500/23

or x = 1413.04 kg (approx)

So mixture contains 1413.04 kg of first ingredient and 1086.96 kg of second ingredient.

Answer 2

Let the quantities of the two ingredients be x and y kg.

x+y=2500.

Total cost of the mixture=1.4x+3.7y dollars.

Total cost of 2500kg=2500×2.4=$6000.

y=2500-x, and 1.4x+3.7(2500-x)=6000.

1.4x+9250-3.7x=6000,

9250-6000=3.7x-1.4x=2.3x.

So x=3250/2.3=1413kg (approx).

y=2500-1413=1087kg.