Your making maple syrup. You mix 5 cent and 25 cent maple syrup. You make 128 ounces that cost 18 cents an ounce. You much of each maple syrup ws required?

Question

Your making maple syrup. You mix 5 cent and 25 cent maple syrup. You make 128 ounces that cost 18 cents an ounce. You much of each maple syrup ws required?

Answer 1

Suppose you're using C ounces of Cheap and E ounces of Expensive syrup. Then:

C + E = 128
5C + 25E = 18 x 128

Multiply the first equation by 5, and you'll get:
5C + 5E = 5 x 128

so:
(5C + 25E) - (5C + 5E) = 20E = (18-5) x 128 = 13 x 128
so E = 13 x 128 / 20 = 83.2
so C = 128 - 83.2 = 44.8

Check it: C costs 5 cents/ounce and E costs 25 cents/ounce, so the total cost is:
(5 x 44.8) + (25 x 83.2) = 2304 cents, and the total amount of syrup is 44.8+83.2=128 ounces, so the cost is 2304 cents divided by 128 ounces = 18 cents per ounce.

Answer 2

To find out how much of each maple syrup is required, let's assign variables to represent the quantities of 5 cent maple syrup and 25 cent maple syrup.

Let's say:
x = quantity (in ounces) of 5 cent maple syrup
y = quantity (in ounces) of 25 cent maple syrup

Given that you mixed a total of 128 ounces of maple syrup, we can write the equation:
x + y = 128 (Equation 1)

We are also given that the cost of making the maple syrup is 18 cents per ounce. Therefore, the total cost of the maple syrup mixture can be expressed as:
(0.05x + 0.25y) = 18

To simplify this equation, we can multiply both sides by 100 to remove the decimal:
5x + 25y = 1800 (Equation 2)

Now we have a system of equations:
Equation 1: x + y = 128
Equation 2: 5x + 25y = 1800

To solve this system of equations, we can use the method of substitution or elimination. Let's use substitution.

From Equation 1, we can express x in terms of y:
x = 128 - y

Now substitute the value of x in Equation 2:
5(128 - y) + 25y = 1800

Expanding and simplifying the equation:
640 - 5y + 25y = 1800
20y = 1800 - 640
20y = 1160
y = 1160 / 20
y = 58

Now substitute the value of y back into Equation 1 to find x:
x + 58 = 128
x = 128 - 58
x = 70

Therefore, you would require 70 ounces of 5 cent maple syrup and 58 ounces of 25 cent maple syrup to make a total of 128 ounces of maple syrup that costs 18 cents per ounce.