how many ninths does it take to make the same amount as 1/3.Explain your answer in words and pictures
1 answer:
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Answer:
120 kg of 30% fat-content chocolate and 30 kg of 40% fat-content chocolate.
Step-by-step explanation:
We are given that a candy distributor needs to mix a 30% fat-content chocolate with a 40% fat-content chocolate to create 150 kilograms of a 32% fat-content chocolate.
Let the amount of 30% fat-content chocolate be 'x' and the amount of 40% fat-content chocolate be 'y'.
So, according to the question;
x + y = 150 ------------ [equation 1]
and
x = 120 kg
Now, putting the value of x in equation 1, we get;
x + y = 150
120 + y = 150
y = 30 kg
Hence, 120 kg of 30% fat-content chocolate and 30 kg of 40% fat-content chocolate.
Ok so for part a we're going to use substitution, since both equations have y alone.
Step 1: Use substitution
y = x - 1 y = -x + 3
x - 1 = -x + 3
If you think about it, this makes sense. You're looking for the point where they intersect, and you know that the y coordinate for that point will be the same in both equations. Therefore, we can set the rest of the equations equal to each other. Now we just need to simplify.
Step 2: add x to each side
x - 1 + x = -x + 3 + x
The x's on the right cancel out so we get:
2x - 1 = 3
Step 4: Add 1 to each side
2x - 1 + 1 = 3 + 1
2x = 4
Step 5: Divide both sides by 2
2x/2 = 4/2
x = 2
Step 6: Plug this x value back into one of the original equations to find the y coordinate
y = x - 1
y = 2 - 1
y = 1
Therefore your answer to part a is (2,1)
I've graphed the solution and attached it. It shouldn't be too hard to replicate - just draw both lines and they should intersect at (2,1)
Hope that helps! If you need clarification or anything please feel free to ask :)
