Phil, the orange juice producer, has to find out how many liters of 15 percent orange juice and 52 percent sugar syrup are needed to create 500 liters of fruit juice containing 25 percent sugar. Fill in the following square to find how many liters of juice and syrup are needed. Round to nearest whole number.

Question

Phil, the orange juice producer, has to find out how many liters of 15 percent orange juice and 52 percent sugar syrup are needed to create 500 liters of fruit juice containing 25 percent sugar. Fill in the following square to find how many liters of juice and syrup are needed. Round to nearest whole number.

Answer 1

To solve this problem, let's assume that Phil needs x liters of 15% orange juice and y liters of 52% sugar syrup.

Since Phil needs to create 500 liters of fruit juice containing 25% sugar, we can set up the following equation:

0.15x + 0.52y = 0.25(500)

Simplifying the equation:

0.15x + 0.52y = 125

Now we can solve the equation to find the values of x and y.

Answer 2

To solve this problem, we need to set up an equation based on the given information.

Let's assume:
x = liters of 15% orange juice
y = liters of 52% sugar syrup

We are given three pieces of information:

1. Total volume: x + y = 500 (equation 1)

2. Sugar content: 0.15x + 0.52y = 0.25 * 500 (equation 2)

Now, let's solve the system of equations:

From equation 1, we can rewrite it as x = 500 - y and substitute it into equation 2:

0.15(500 - y) + 0.52y = 125

75 - 0.15y + 0.52y = 125

0.37y = 50

y ≈ 135

Plug the value of y back into equation 1 to find x:

x = 500 - y
x = 500 - 135
x ≈ 365

So, approximately 365 liters of 15% orange juice and 135 liters of 52% sugar syrup are needed to create 500 liters of fruit juice containing 25% sugar.

Answer 3

To solve this problem, we can use a system of equations. Let's represent the unknown quantities as variables:

Let x represent the number of liters of 15% orange juice.
Let y represent the number of liters of 52% sugar syrup.

Since we need to create a total of 500 liters of fruit juice, we have the equation:

x + y = 500 (Equation 1)

Additionally, we need the final mixture to contain 25% sugar. The sugar content in the mixture can be calculated by multiplying the volume of each ingredient by its respective sugar concentration. So, the equation for the sugar content is:

0.15x + 0.52y = 0.25 * 500 (Equation 2)

Now, we can solve this system of equations to find the values of x and y.

Step 1: Solve Equation 1 for x:
x = 500 - y

Step 2: Substitute the value of x in Equation 2:
0.15(500 - y) + 0.52y = 0.25 * 500

Step 3: Simplify and solve for y:
75 - 0.15y + 0.52y = 125
0.37y = 50
y = 50 / 0.37 ≈ 135.14

Step 4: Round y to the nearest whole number:
y ≈ 135

Step 5: Substitute the value of y into Equation 1 to find x:
x + 135 = 500
x ≈ 500 - 135
x ≈ 365

Therefore, Phil needs approximately 365 liters of 15% orange juice and 135 liters of 52% sugar syrup to create 500 liters of fruit juice containing 25% sugar.