SOLUTION: a certain mixture is made by mixing two ingredients in the ratio 7 to 8. if it is required to make 30 pounds of mixture, how much of each ingredient will be needed? The first poun

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Question 413042: a certain mixture is made by mixing two ingredients in the ratio 7 to 8. if it is required to make 30 pounds of mixture, how much of each ingredient will be needed? The first pound and second pound ?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
2 ingredients:
let x = amount of first ingredient.
let y = amount of second ingredient.

they are in a ratio of 7 to 8.

this means that x/y = 7/8

multiply both sides of this equation by (8/7)*y to get:

8/7 * x = y

if the new mixture contains 30 pounds, then x + y = 30

substitute 8/7*x for y to get:

x + 8/7*x = 30

multiply both sides of this equation by 7 to get:

7x + 8x = 30*7 which becomes:

15x = 30*7

divide both sides of this equation by 15 to get:

x = 30/15 * 7 = 2 * 7 = 14

since x + y = 30, then y = 16

you get:

x = 14 = number of pounds in first ingredient.
y = 16 = number of pounds in second ingredient.

x + y = 14 + 16 = 30 (good)
x/y = 14/16 = 7/8 (good)

that's your answer.

number of pounds of first ingredient is 14.
number of pounds of second ingredient is 16.