The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains pure fruit juice. How many pints of each of the two existing types of drink must be used to make pints of a mixture that is pure fruit juice

Complete question:

The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% 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 50 pints of a mixture that is 70% pure fruit juice?

Juice A = 15

Juice B = 35

Step-by-step explanation:

Given the following:

Juice A:

Let juice A = a

35% pure fruit juice

Juice B:

Let juice B = b

85% pure fruit juice

We need to make 50 pints of juice from both: that is ;

a + b = 50 (1)

In terms of pure fruit:

a = 0.35 ; b = 0.85 ;

Our mixed fruit juice from a and b should be 70% pure fruit = 0.7

Mathematically,

0.35a + 0.85b = 50(0.7)

0.35a + 0.85b = 35 (2)

Multiply (2) by 100

35a + 85b = 3500 (3)

We can then solve the simultaneous equation:

a + b = 50 (1)

35a + 85b = 3500 (3)

Multiply (1) by 35

35a + 35b = 1750 (4)

35a + 85b = 3500 ---(5)

Subtract (5) from (4)

-50b = -1750

b = 35

Substitute b = 35 into (2)

0.35a + 0.85(35) = 35

0.35a + 29.75 = 35

0.35a = 35 -29.75

0.35a = 5.25

a = 5.25/0.35

a = 15

Juice A = 15

Juice B = 35

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.

true

step-by-step explanation: