Question

10) After hearing that the children were dreaming of sugar plums in "The Night

Before Christmas," Cindy Lou wonders just how much time the kids were dreaming
during their slumber. If the children were asleep from 7.5 to 10 hours, and 25% of
their sleep includes dreams, how much time was spent dreaming of sugar plums?
Write a compound inequality for this situation and solve. Show your answer on a
graph too

Answer 1

First, let's find the total amount of time the children spent asleep: 10 hours - 7.5 hours = <<10-7.5=2.5>>2.5 hours

Then, let's find the amount of time the children spent dreaming by multiplying the total amount of time they spent asleep by 25%: 2.5 hours * 25% = <<2.525.01=.625>>.625 hours

We can represent this situation with the compound inequality: .625 hours <= x <= 2.5 hours

To graph this inequality, we can plot a point at 2.5 on the number line and shade in the region to the left of it. Then, we can plot a point at .625 on the number line and shade in the region to the right of it. The solution to the inequality is the region where both shaded regions overlap.

[asy]

unitsize(1 cm);

draw((-2,0)--(4,0));

draw((0,-1)--(0,1));

draw((-.2,0)--(0,.2)--(.2,0)--(0,-.2)--cycle);

draw((2.5,-1)--(2.5,1),dashed);

draw((.625,-1)--(.625,1),dashed);

label("$x$",(4,0),SE);

fill((-2,0)--(-2,1)--(2.5,1)--(2.5,0)--cycle,gray(.7));

fill((2.5,0)--(2.5,1)--(4,1)--(4,0)--cycle,gray(.7));

[/asy]

Explanation: