Question

from unit 4, lesson 13
match each sentence with the inequality that could represent the situation.
a han got $2 from clare, but still has less than $20.
1 ( x - 2 < 20 )
b mai spent $2 and has less than $20.
2 ( 2x < 20 )
c if tyler had twice the amount of money he has, he would have less than $20.
3 ( x + 2 < 20 )
d if priya had half the money she has, she would have less than $20.
4 ( \frac{1}{2}x < 20 )
from unit 4, lesson 12
at a skateboard shop:
a. the price tag on a shirt says $12.58. sales tax is 7.5% of the price. how much will the shirt cost including tax?
b. the shop buys a helmet for $19.00 and sells it for $31.50. what percentage was the markup?
c. the shop pays workers $14.25 per hour plus 5.5% commission. if someone works 18 hours and sells $250 worth of merchandise, what is the total earning on their paycheck for this pay period? explain or show your reasoning.

Explanation:

First Problem: Matching Sentences to Inequalities

Step1: Analyze Sentence A

Let $x$ = Han's original money. He gains $2$, so total is $x+2$, which is less than 20.
Matches: $x + 2 < 20$ (Inequality 3)

Step2: Analyze Sentence B

Let $x$ = Mai's original money. She spends $2$, so total is $x-2$, which is less than 20.
Matches: $x - 2 < 20$ (Inequality 1)

Step3: Analyze Sentence C

Let $x$ = Tyler's money. Twice his money is $2x$, which is less than 20.
Matches: $2x < 20$ (Inequality 2)

Step4: Analyze Sentence D

Let $x$ = Priya's money. Half her money is $\frac{1}{2}x$, which is less than 20.
Matches: $\frac{1}{2}x < 20$ (Inequality 4)

Part a

Step1: Calculate tax amount

Tax = $12.58 \times 0.075$
$\text{Tax} = 12.58 \times 0.075 = 0.9435$

Step2: Add tax to base price

Total cost = $12.58 + 0.9435$
$\text{Total Cost} = 12.58 + 0.9435 = 13.5235$

Part b

Step1: Calculate markup amount

Markup = $31.50 - 19.00$
$\text{Markup} = 31.50 - 19.00 = 12.50$

Step2: Find markup percentage

% Markup = $\frac{12.50}{19.00} \times 100$
$\text{\% Markup} = \frac{12.50}{19.00} \times 100 \approx 65.79$

Part c

Step1: Calculate hourly earnings

Hourly pay = $14.25 \times 18$
$\text{Hourly Pay} = 14.25 \times 18 = 256.50$

Step2: Calculate commission amount

Commission = $250 \times 0.055$
$\text{Commission} = 250 \times 0.055 = 13.75$

Step3: Sum earnings for total pay

Total pay = $256.50 + 13.75$
$\text{Total Pay} = 256.50 + 13.75 = 270.25$

Answer:

A → 3
B → 1
C → 2
D → 4

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Second Problem: Skateboard Shop Calculations