The owner of a health food store combined cranberry juice that cost $7.79 per quart with apple juice that cost $7.19 per quart. how many quarts of each were used to make 10 quarts of cranberry juice mixture costing $7.61 per quart
7.79x + 7.19(10-x) = 7.61(10)
x = 7
so,
7 quarts at 7.79
3 quarts at 7.19
makes sense, since 7.61 is near to 7.79
To find the number of quarts of cranberry juice and apple juice used, we can set up a system of equations based on the given information.
Let's assume that the owner used x quarts of cranberry juice and (10 - x) quarts of apple juice, where x is the number of quarts of cranberry juice used.
The cost of the cranberry juice is $7.79 per quart, and the cost of the apple juice is $7.19 per quart. The resulting mixture costs $7.61 per quart.
Using these values, we can set up the following equation to represent the cost of the mixture:
(x * $7.79) + ((10 - x) * $7.19) = 10 * $7.61
Now, let's solve this equation to find the value of x:
7.79x + 7.19(10 - x) = 76.1
7.79x + 71.9 - 7.19x = 76.1
0.6x = 4.2
x ≈ 7
Therefore, the owner used approximately 7 quarts of cranberry juice and 3 quarts of apple juice to make a 10-quart cranberry juice mixture costing $7.61 per quart.