Afactory makes an oil mixture by mixing oils of grades a and b as follows. for every 2.3 liters of grade a oil, 1.2 liters of grade b oil are mixed in. how many liters of grade a oil and grade b oil will the factory need to make 1000 liters of their oil mixture? explain your solution.

The ratio is 2.3:1.2 for A:B. Ratios will remain the same but can be scaled up or down by some factor/multiple. Like if you had a food recipe that you needed to double, the scaling factor would be 2 and all ingredients in the recipe would be doubled.

Since we don't know the scaling factor, we assign that multiple "x". Then the amounts of each ingredient oil would be:

amount of A = 2.3x
amount of B = 1.2x

add them together to get the required mixture amount.

1000 = 2.3x + 1.2x
1000 = 3.5x
1000/3.5 = x
285.7 = x
this is the scaling factor.

plug x in to find the amounts of each oil type.

A = 2.3(285.7)
A = 657.1 L

B = 1.2(285.7)
B = 342.9 L