a granola mix contains 25 nuts How many ounces of nuts must

a granola mix contains 25% nuts. How many ounces of nuts must be added to get 10 ounces of granola with 40% nuts

Solution

Let x be the number of ounces of nuts to be added to get 10 ounces of granola with 40 % nuts.

Let y be the existing weight ( in ounces) of granola mix with 25 % nuts. The weight of nuts in this granola mix is 0.25y. After adding x ounces of nuts, the weight of granola mix is y + x . Therefore , y + x = 10...(1)

The weight of nuts in the the current granola mix is 0.4 ( x + y). Since we have added x ounces of nuts to the earlier granola mix, we have 0.25y + x = 0.4( x + y). On multiplying both the sides by 100, we have 25y + 100x = 40 (x + y) or, 25y + 100x = 40x + 40y or, 100x - 40 x = 40y - 25y or, 60x = 15 y or, x = 15/60 y or, x = 1/4y...(2).On substituting this value of x in the 1st equation, we get 1/4y + y = 10 or, 5/4(y) = 10 or, y = (10*4)/5 or, y = 8 . Therefore, x = 1/4 y = 2 . Thus, we should add 2 ounces of nuts to 8 ounces of existing granola mix with 25 % nuts to get 10 ounces of granola mix with 40 % nuts.