Exercise 30 Page 246

We can first find the number of exercises we already finished to find how many we still need to do. This means finding 75% of 32. Recall that the percent proportion is a proportion that sets the ratio of a part of a whole equal to the ratio of a percent out of 100. We can represent a is p percent of wwith the given proportion. part/whole=percent/100 ⇔ a/w=p/100We can find what 75% of 32 is by thinking about 75 as the percent and 32 as the whole. Let's substitute p= 75 and w= 32 into the formula and solve for a using the Properties of Equality.

a/w=p/100

SubstituteII

p= 75, w= 32

a/32=75/100

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Solve for a

MultEqn

LHS * 32=RHS* 32

a/32* 32=75/100 * 32

FracMultDenomToNumber

a/32* 32 = a

a=75/100 * 32

MoveRightFacToNum

a/c* b = a* b/c

a=75* 32/100

Multiply

Multiply

a=2400/100

CalcQuot

Calculate quotient

a= 24

Knowing the value of a, let's look at the completed percent proportion. 24/32=75/100 We found that 24 is 75 % of 32. This means that we already finished 24 out of assigned 32 exercises. Now, we can subtract 24 from 32 to find how many more we still need to complete. 32-24=8 This means we have 8 more exercises left to do after dinner.

Checking Our Answer

Checking Our Answer

We can use a model to check our answer.