FDP Guide 6th Edition page 86

[Sadatentertainment]

The Crandall's hot tub has a capacity of x liters and is half full. Their swimming pool, which has a capacity of y liters, is filled to four-fifths of its capacity. If enough water is drained from the swimming pool to fill the hot tub to capacity, the pool is now how many liters short of full capacity, in terms of x and y?

A. 0.8y-0.5x
B. 0.8y+0.5x
C. 0.2y + 0.5x
D. 0.3(y-x)
E. 0.3(y+x)

How do I solve this problem algebraically? The guide shows how to using smart numbers.

[Chelsey Cooley]

The Crandall's hot tub has a capacity of x liters and is half full. Their swimming pool, which has a capacity of y liters, is filled to four-fifths of its capacity. If enough water is drained from the swimming pool to fill the hot tub to capacity, the pool is now how many liters short of full capacity, in terms of x and y?

A. 0.8y-0.5x
B. 0.8y+0.5x
C. 0.2y + 0.5x
D. 0.3(y-x)
E. 0.3(y+x)

How do I solve this problem algebraically? The guide shows how to using smart numbers.

I recommend against solving this one algebraically! But if you choose to, start by writing out a table showing all of the values you're given, in terms of x and y.

Current water in hot tub: 0.5x
Current water in swimming pool: 0.8y

Water needed to fill hot tub: x - 0.5x = 0.5x
Water remaining in swimming pool, AFTER hot tub is filled: 0.8y - 0.5x

Full capacity of swimming pool: y

To find how short of capacity the swimming pool is, take the full capacity, and subtract the amount of water that's in it:

full capacity - remaining water
y - (0.8y - 0.5x)
0.2y + 0.5x