Answer: 20 fluid ounces of tomato paste
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Work Shown
x = amount of water
y = amount of tomato paste
x+y = 35
y = 35-x
x : y = x : (35-x)
x/(35-x) = 3/4
4x = 3(35-x)
4x = 105-3x
4x+3x = 105
7x = 105
x = 105/7
x = 15
y = 35-x
y = 35-15
y = 20
You need 15 fluid ounces of water and 20 fluid ounces of tomato paste to make 35 fluid ounces of sauce.
Note how the ratio 15:20 reduces to 3:4 after you divide both parts by the GCF 5.
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An alternative approach
3:4 is the initial ratio of water to tomato paste
multiply both parts by x and we have
3x:4x
the individual parts add up to 35 total, so
3x+4x = 35
7x = 35
x = 35/7
x = 5
So 3x:4x turns into 15:20 after we plug in x = 5
we have 15 parts water, 20 parts tomato paste