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NNADVOKAT [17]
3 years ago
14

How many kilograms of a 5% salt solution and how many kilograms of a 15% salt solution must be mixed together to make 45kg of an

8% salt solution?
Mathematics
1 answer:
JulsSmile [24]3 years ago
5 0

Answer:

31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

Step-by-step explanation:

Let us assume that the number of kilograms of a 5% salt solution used be x .

Let us assume that the number of kilograms of a 15% salt solution used be y .

As given

A 5% salt solution and 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

Equation becomes

x + y = 45

5% is written in the decimal form .

= \frac{5}{100}

= 0.05

15% is written in the decimal form .

= \frac{15}{100}

= 0.15

8% is written in the decimal form .

= \frac{8}{100}

= 0.08

Thus

Concentration of 5% salt solution × Number of kilograms of 5% salt solution used + Concentration of 15% salt solution × Number of kilograms of  15% solution used = Concentration of 8% salt solution × Number of kilograms of 8% salt solution

Thus

0.05x + 0.15y = 0.08 × 45

Simplify the above

\frac{5x}{100} + \frac{15y}{100} = \frac{8\times 45}{100}

5x + 15y = 360

Thus two equations becomes

x + y = 45

5x + 15y = 360

Multiply x + y = 45 by 5 and subtracted from 5x + 15y = 360 .

5x - 5x + 15y - 5y = 360 - 225

10y = 135

y = \frac{135}{10}

y = 13.5 kilograms

Put value of y in the equation

x + 13.5 = 45

x = 45 - 13.5

x = 31.5 kilograms

Therefore the 31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

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