Strategy #15 The Sum of the Parts Equals the Whole
The way this usually comes up is when we know, let’s say, the total distance, and this distance is broken into two unknown parts. We need expressions for the two parts, but we don’t want to introduce a second variable. Rather, we want to express one of the variables in terms of the other variable.
We will label one of the parts as X. Then, we will label the other part as Total Distance – X.
Example 1 (Practice Test 7)
Calculator ok
The two parts in this problem are the volume of pieces of fruit and the volume of syrup. So, the sum of the parts equals the whole is:
fruit + syrup = volume of can.
Since we want fruit turn this equation around to solve for fruit:
fruit = volume of can — syrup.
Remember that the formula for the volume of a cylinder is given in the reference section at the beginning of each math section: area of base x height of cylinder = volume.
volume of fruit = (75 sq cm)(10 cm) — 110 cubic cm = 640 cubic cm. Choice C is correct.