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Big Ideas Math Algebra 1, 2015 View details

Chapter Test

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Exercise 18 Page 97

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a We are told that the tax applies only to the difference between the price of the item and $175. We can see from the receipt that the price of the suit is $295. This difference is the taxable amount.

295 - 175 = 120 We will now find what percent of this amount is 7.50. This can be done using a percent proportion.

Part/Whole=Percent/100

SubstituteValues

Substitute values

7.50/120=x/100

▼

Solve for x

WriteDec

Write as a decimal

0.0625=x/100

MultEqn

LHS * 100=RHS* 100

6.25=x

RearrangeEqn

Rearrange equation

x=6.25

Therefore, the tax rate is 6.25 %.

b To find the possible prices p of coats that the shopper can afford we need to consider the sales tax. Since the shopper can spend at most $430, we can write an inequality for this situation.

p+Sales Tax≤$430 We are told that the sales tax applies only to the difference between the price p of the item and 175. We found in Part A that the tax rate is 6.25 %, which can be rewritten as the decimal value 0.0625. Sales Tax = 0.0625(p-175) We can use this to rewrite our inequality. p+0.0625(p-175)≤430 Let's solve this inequality for p.

p+0.0625(p-175)≤430

▼

Solve for p

Distr

Distribute 0.0625

p+0.0625p-0.0625(175) ≤ 430

UseCalc

Use a calculator

p+0.0625p-10.9375≤430

AddTerms

Add terms

1.0625p-10.9375≤430

AddIneq

LHS+10.9375≤RHS+10.9375

1.0625p≤440.9375

DivIneq

.LHS /1.0625.≤.RHS /1.0625.

p≤440.9375/1.0625

UseCalc

Use a calculator

p≤415

This means that when taxes are included the shopper can afford any winter coats that cost less than or equal to $415.

c We want to find for which values of p the flat 5 % tax is cheaper than the 6.25 % tax on purchases over $175.

0.05p < 0.0625(p-175) Let's solve this inequality for p.

0.05p<0.0625(p-175)

▼

Solve for p

DivIneq

.LHS /0.05.<.RHS /0.05.

p<0.0625(p-175)/0.05

MovePartNumRight

a* b/c=a/c* b

p<0.0625/0.05(p-175)

UseCalc

Use a calculator

p<1.25(p-175)

Distr

Distribute 1.25

p<1.25p-1.25(175)

UseCalc

Use a calculator

p<1.25p-218.75

SubEqn

LHS-1.25p=RHS-1.25p

p-1.25p<-218.75

SubTerm

Subtract term

-0.25p<-218.75

DivNegIneq

Divide by -0.25 and flip inequality sign

p>-218.75/-0.25

DivNegNeg

- a/- b=a/b

p>218.75/0.25

UseCalc

Use a calculator

p>875

Any item costing more than $875 will be cheaper if purchased in the state with a flat 5 % sales tax rate. Three example prices are $945, $1200, and $1500.

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Exercises p.97

Exercise 18 Page 97

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