Question

How many quarts of olive oil did they use? (see below) Thanks!

Answer 1

Solved for one of the volumes. I will let you solve for the other by subtraction.

Explanation:

`color(blue)("Building the model")`

To maintain a high level of precision I will stick with fractions.
Rounding decimals can lead to accumulated errors. So if you wish to use decimals convert the fractions at the very end.

Let the volume of 30% oil be `v_30`
Let the volume of 79% oil be `v_79`
Let the volume of the blended be `v_b = 19/20" "`quarts

For now ignore the units of quarts.

When blended for total volume we have:

`v_30+v_79=19/20 " "......................Equation(1)`

When blended for % of oil volume content we have (in quarts):

`[30/100xxv_30]+[79/100xxv_79] =[(40 6/19)/100 xx19/20]....Equation(2)`
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`color(blue)("Answering the question")`

In `Eqn(2)` we have 2 unknowns. If we can express one of these in terms of the other we end up with just 1 unknown. Thus solvable.

I choose to substitute for `v_79`

From `Equation(1)`

`v_79=19/20-v_30" "....................Equation(3)`

Using `Equation(3)` substitute for `v_79` in `Equation(2)`

`[30/100xxv_30]+[79/100xx(19/20-v_30)] =[(40 6/19)/100 xx19/20]`

`color(white)(d"d")(30v_30)/100color(white)("dd.d")+color(white)("ddd")1501/2000-(79v_30)/100 color(white)("ddd")= color(white)("ddd")(766)/2000`

Having a common denominator of 2000 gives:

`(600v_30)/2000 +1501/2000-(1580v_30)/2000=766/2000`

Multiply both sides by 2000

`600v_30+1501-1580v_30=766`

`-980v_30=-2267`

`color(green)(v_30=(-2267)/(-980) = 2 307/980 "quarts "...................Equation(3))`
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Using `Equation(3)` substitute for `v_30" in "Equation(1)`

I will let you finish that off.