Question

make sure to show all work.

1. what is 25% of 90?
2. what is 33% of 55?
3. simplify the following expression: -2(3x + 2) + 5x
4. are the following ratios proportional? \\(\frac{3}{5}\\) and \\(\frac{6}{15}\\)
5. what is the value of the expression shown below when x = 5 and y = -2? 4y - 2x + 7
6. solve and graph the inequality: 2x + 4 ≥ 24

extended response

1. denim orders pictures from a photographer. each picture costs $6.75. a one time shipping fee of $4.50 is added to the cost of the order. the total cost of denim’s order before tax is $126.00. how many pictures did denim order?

Explanation:

Step1: Solve 25% of 90

Convert 25% to decimal: $0.25 \times 90$

Step2: Solve 33% of 55

Convert 33% to decimal: $0.33 \times 55$

Step3: Simplify $-2(3x+2)+5x$

Distribute then combine like terms: $-6x -4 +5x = -x -4$

Step4: Check proportionality of $\frac{3}{5}$ and $\frac{6}{15}$

Cross-multiply: $3 \times 15 = 45$, $5 \times 6 = 30$; $45
eq 30$

Step5: Evaluate $4y-2x+7$ at $x=5,y=-2$

Substitute values: $4(-2) -2(5) +7 = -8 -10 +7$

Step6: Solve $2x + 4 \geq 24$

Isolate $x$: $2x \geq 20 \implies x \geq 10$

Step7: Solve for number of pictures

Set up equation: $6.75n + 4.50 = 126$; solve for $n$: $6.75n = 121.5 \implies n = \frac{121.5}{6.75}$

Answer:

1. $22.5$
2. $18.15$
3. $-x -4$
4. No
5. $-11$
6. $x \geq 10$ (Graph: Closed circle at 10, arrow pointing right on the number line)
7. 18