Question

assessment practice

1. last month nicole spent $30. this month she spent 140% of wh

write a proportional equation to represent the situation. how n
this month?

1. mr. jones, the owner of a small store buys kayak paddles for $50

for 180% of the purchase price.
part a
a customer buys a paddle for $97.65, which
includes the selling price and sales tax. what is
the sales tax rate?
a 7.65%
b 4.7%
c 9.75%
d 8.5%
part b
if mr. jone
uses the sa
paddles m
before tax

154 3-2 connect percent and proportion

Explanation:

Question 18 (assuming the full question is "This month she spent 140% of what she spent last month. Write a proportional equation to represent the situation. How much did she spend this month?")

Step1: Define variables

Let \( l \) be last month's spending (\( l = 30 \)) and \( t \) be this month's spending. The proportion is based on percentage: \( \frac{t}{l}=\frac{140}{100} \).

Step2: Substitute \( l = 30 \)

Substitute \( l = 30 \) into the equation: \( \frac{t}{30}=\frac{140}{100} \).

Step3: Solve for \( t \)

Cross - multiply: \( 100t=30\times140 \). Then \( 100t = 4200 \), so \( t=\frac{4200}{100}=42 \).

Step1: Find the selling price before tax

Mr. Jones buys the paddle for \( \$50 \) and sells it for 180% of the purchase price. The selling price before tax (\( s \)) is \( s = 50\times\frac{180}{100}=50\times1.8 = 90 \).

Step2: Let the tax rate be \( r \) (in decimal)

The total price paid by the customer is the selling price plus tax: \( 90(1 + r)=97.65 \).

Step3: Solve for \( r \)

Divide both sides by 90: \( 1 + r=\frac{97.65}{90}=1.085 \). Then \( r=1.085 - 1=0.085 \), which is \( 8.5\% \) when converted to percentage.

Answer:

Proportional equation: \( \frac{t}{30}=\frac{140}{100} \), This month's spending: \( \$42 \)

Question 19 Part A