Gigi wants to sell 18 kilograms of a cookie mix for $7 a kilogram. She starts with a $5 cookie mix and a $10 cookie mix. How many kilograms of each does she need to make the final mix?
amount of cheaper mix --- x kg
amount of expensive mix -- 18-x
solve for x and sub into my definitions
5x + 10(18-x) = 7(18)
To solve this problem, we need to set up a system of equations. Let's represent the number of kilograms of the $5 cookie mix as 'x' and the number of kilograms of the $10 cookie mix as 'y'.
Since Gigi wants to sell 18 kilograms of the final cookie mix, we have the equation:
x + y = 18 -- (Equation 1)
She wants to sell the mix for $7 per kilogram. To determine the total cost, we need to multiply the cost of each cookie mix (per kilogram) by the number of kilograms of that mix. The total cost equation is:
5x + 10y = 7 * 18 -- (Equation 2)
Now, we have a system of equations:
x + y = 18 -- (Equation 1)
5x + 10y = 7 * 18 -- (Equation 2)
To solve this system, we can use the method of substitution or elimination. Let's use substitution:
From Equation 1, we can express x in terms of y:
x = 18 - y
Now, substitute this value of x into Equation 2:
5(18 - y) + 10y = 7 * 18
90 - 5y + 10y = 126
5y = 126 - 90
5y = 36
y = 36 / 5
y = 7.2
Now, we know that y = 7.2 kilograms of the $10 cookie mix. Substitute this value of y back into Equation 1 to find x:
x + 7.2 = 18
x = 18 - 7.2
x = 10.8
Therefore, Gigi needs 10.8 kilograms of the $5 cookie mix and 7.2 kilograms of the $10 cookie mix to make the final mix.