write an equation for the problem and solve the problem. How much 15% solution and how much 45% solution should be combined to make 30 liters of 35% solution?

Amount of 15% solution = 10 litres

Amount of 45% solution = 20 litres

This is based on simultaneous equations.

Let x represent the amount of the 15% solution.

Let y represent the amount of the 45% solution. Thus;

0.15x + 0.45y = 0.35(x + y) - - - (eq 1)

Since they both combine to make 30 litres solution, then;

x + y = 30 - - - (eq 2)

From eq(2), let's make x the subject to get; x = 30 - y

Putting 30 - y for x in eq 1 gives;

0.15(30 - y) + 0.45y = 0.35(30 - y + y)

4.5 - 0.15y + 0.45y = 10.5

Rearranging gives;

0.3y = 6

y = 6/0.3

y = 20 litres

Putting 20 for y in eq 2 gives;

x + 20 = 30

x = 30 - 20

x = 10 litres

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so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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