Question 413042
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.