Math  /  Algebra

Question13. Last year Conner paid 15%15 \% of his earmings in federal taxes. He paid $3000\$ 3000. Jose also paid 15%15 \% of his earnings in federal taxes, but he paid $3600\$ 3600. How much more did lose earn than Conner? (A) $4000\$ 4000 (c) $20,000\$ 20,000 (B) $6000\$ 6000 (D) $24,000\$ 24,000
14. The tahle shows the price of a bus ticket based on the number of miles traveled. Which equation represents the relationship between the ticket price pp and the number of miles traveled mm ? (F) p=2mp=2 m \begin{tabular}{|c|c|} \hline Miles & Price \\ \hline 100 & $50\$ 50 \\ \hline 150 & $70\$ 70 \\ \hline 200 & $90\$ 90 \\ \hline 250 & $110\$ 110 \\ \hline \\ \hline \end{tabular} (6) p=0.5mp=0.5 m (H) p=2π+10p=2 \pi+10 (I) p=0.4m+10p=0.4 m+10
15. During a trip, Josh recorded the amount of time it took him to travel the distances shown in the table below. \begin{tabular}{|l|c|c|c|c|} \hline Time (hours) & 2 & 5 & 7 & 8 \\ \hline Distance (miles) & 60 & 150 & 210 & 240 \\ \hline \end{tabular}

Which equation represents the relationship between distance dd and time tt ? (A) d=30td=30 t (C) d=30+td=30+t (B) t=30dt=30 d (D) t=d+30t=d+30
16. A stepped-out solution is shown below. 3(3x1)3(5x3)=49x315x+9=46x+6=46x+66=466x=26x6=26x=13\begin{aligned} 3(3 x-1)-3(5 x-3) & =4 \\ 9 x-3-15 x+9 & =4 \\ -6 x+6 & =4 \\ -6 x+6-6 & =4-6 \\ -6 x & =-2 \\ \frac{-6 x}{-6} & =\frac{-2}{-6} \\ x & =\frac{1}{3} \end{aligned}  Step 19x315x+9=4 Step 26x+6=4\begin{array}{lr} \text { Step } 1 & 9 x-3-15 x+9=4 \\ \text { Step } 2 & -6 x+6=4 \end{array}

Step 3 Step 4 Step 5 Step 6 Which property justifies Step 1? (F) Division Property of Equality (G) Suburaction Property of Equality (H) Commutative Property (I) Distributive Property

Studdy Solution

STEP 1

1. Conner and Jose both paid 15% of their earnings in federal taxes.
2. We need to find the difference in earnings between Conner and Jose.
3. The relationship between ticket price and miles traveled is linear.
4. The relationship between distance and time is linear.
5. We need to identify the property used in Step 1 of the solution.

STEP 2

1. Calculate Conner's earnings.
2. Calculate Jose's earnings.
3. Determine the difference in earnings.
4. Determine the equation for the bus ticket price.
5. Determine the equation for the distance and time relationship.
6. Identify the property used in Step 1 of the given solution.

STEP 3

Calculate Conner's earnings:
Conner paid $3000, which was 15% of his earnings. Let \( E_C \) be Conner's earnings.
0.15×EC=3000 0.15 \times E_C = 3000
Solve for EC E_C :
EC=30000.15=20000 E_C = \frac{3000}{0.15} = 20000

STEP 4

Calculate Jose's earnings:
Jose paid $3600, which was 15% of his earnings. Let \( E_J \) be Jose's earnings.
0.15×EJ=3600 0.15 \times E_J = 3600
Solve for EJ E_J :
EJ=36000.15=24000 E_J = \frac{3600}{0.15} = 24000

STEP 5

Determine the difference in earnings:
Difference=EJEC=2400020000=4000 \text{Difference} = E_J - E_C = 24000 - 20000 = 4000
Thus, Jose earned $4000 more than Conner.

STEP 6

Determine the equation for the bus ticket price:
The table shows a linear relationship between miles traveled and ticket price. We can calculate the slope m m using two points, say (100, 50) and (150, 70).
m=7050150100=2050=0.4 m = \frac{70 - 50}{150 - 100} = \frac{20}{50} = 0.4
Using the point-slope form, the equation is:
p=0.4m+10 p = 0.4m + 10

STEP 7

Determine the equation for the distance and time relationship:
The table shows a linear relationship between time and distance. Calculate the slope m m using two points, say (2, 60) and (5, 150).
m=1506052=903=30 m = \frac{150 - 60}{5 - 2} = \frac{90}{3} = 30
Using the point-slope form, the equation is:
d=30t d = 30t

STEP 8

Identify the property used in Step 1 of the given solution:
Step 1 simplifies the expression 3(3x1)3(5x3) 3(3x - 1) - 3(5x - 3) to 9x315x+9 9x - 3 - 15x + 9 .
This uses the Distributive Property, which states that a(b+c)=ab+ac a(b + c) = ab + ac .
The answers are:
13. (A) 40004000
14. (I) p=0.4m+10 p = 0.4m + 10
15. (A) d=30t d = 30t
16. (I) Distributive Property

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