The Royal Company

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 60%pure fruit juice, and the second type is 75% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 120 pints of a mixture that is 70% pure fruit juice?

Answer 1

Let x = amount of 60% pure fruit juice and y = amount of 75% pure fruit juice.

You have two unknowns and two equations.

x+y =120

0.60x+0.75y = 0.70(120) = 84

Scale the second equation by 100 and the first equation by 60 and subtract the the first scaled equation from the second scaled equation:

60x + 75y = 8400

-60x - 60y = -7200

------------------------

15y = 1200

y = 1200/15 = 80 pints of the 75% juice

x + 80 = 120

x = 40 pints of the 60% juice

Answer 2

Hi Matilda O

You can set up two equations in two unknowns and use substitution to find your answers,

Let x = 75% juice

Let y = 60% juice

You will need an equation for your total amount of 120 pints

x + y = 120

and 120 - x = y

Next you need will an equation for your total amount of juice in 120 pints

.75x + .60y = .70(120)

and .75x + 60y =84

Your equations are

x + y = 120

.75x + .60y = 84

Now that you have your equations you can substitute

.75x + .60(120 - x) = 84

.75x - .60x + 72 = 82

Now regroup and just solve for x

.15x = 12

x = 12/.15 = 80

y = 120 - x = 120 - 80 = 40

Checking

x + y = 120

80 + 40 = 120

.75(80) + .60(40) = 60 + 24 = 84

Of course, there are other ways of doing this since it is just diluting the 75% down to 70%.

I hope this helps.

Answer 3

.7 x 120 =84, which means that of its 120 pints, the final mixture has 84 pints of pure fruit juice. This gives us two equations:

Let the amount of type 1 be x, and the amount of type 2 be y

x+y = 120

.6x + .75y= 84.

You've got two options here: Solve a system of equations or trial and error until you find 2 numbers that: a) add up to 120 b) work in the equation .6x+.75y = 84.

For the system, set each equation equal to y:

#1) y=-x +120

#2) .75x= -.6x+84

y=-8x + 112.

Now, since both equations add up to y, you can set them equal to each other and solve for x:

-x+120=-8x+112.

Can you solve it from here? Solve for x and then plug it into one of the first two equations (I'd recommend y=-x+120) to solve for y.

Leave a comment if you get stuck and I can help you through the rest.