Question

1. at a sale, soccer cleats were sold for $59.50. if the original price was $70, what percentage off the original price is the sale price?
2. the number of apples in a fruit basket is directly proportional to the number of oranges. if there are 2 apples and 5 oranges in marys basket, how many more apples are there in a basket that contains 35 oranges?
3. what is the value of the constant, n, in the equation below that will result in infinitely many solutions? 4x + 50 = mx+mn
4. what is the smallest value of x that satisfies the equation below? |2x - 1| = 23
5. the table shows the number of calories in a cheeseburger at six different restaurants. what is the median number of calories in cheeseburgers at all six restaurants? calories in a cheeseburger

restaurant	calories
clear lake cafe	900
mollys	740
riverside diner	1,120
mayas bistro	1,050
toms place	700

1. solve for x by clearing the fraction. $\frac{4}{5}x - 7(\frac{1}{2}x + 1)=-3x - 1$
2. what is the solution set to the inequality below? -7(2x + 3)>1 - 4(3x - 2)
3. a group of friends are going to cedar point. they have no more than $350 to spend on parking and admission. if they spend $35 on parking and tickets cost $38 each, what is the maximum number of people who can go to cedar point? inequality: ___ solve:

Explanation:

9.

Step1: Find the amount of discount

The discount amount is the original price minus the sale price. So, $70 - 59.50=10.50$.

Step2: Calculate the percentage - off

The percentage - off formula is $\text{Percentage off}=\frac{\text{Discount amount}}{\text{Original price}}\times100\%$. Substitute the values: $\frac{10.50}{70}\times100\% = 15\%$.

Step1: Set up the proportion

Since the number of apples is directly proportional to the number of oranges, we have the proportion $\frac{a_1}{o_1}=\frac{a_2}{o_2}$, where $a_1 = 2$, $o_1 = 5$, and $o_2=35$.

Step2: Solve for $a_2$

Cross - multiply: $a_2=\frac{a_1\times o_2}{o_1}$. Substitute the values: $a_2=\frac{2\times35}{5}=14$.

Step1: Rewrite the equation for infinite solutions

For the equation $4x + 50=mx+mn$ to have infinitely many solutions, the coefficients of $x$ on both sides must be equal and the constant terms must be equal. So, $m = 4$.

Step2: Find the value of $n$

Substitute $m = 4$ into the constant - term equation $50=mn$. Then $50 = 4n$, and $n=\frac{50}{4}=\frac{25}{2}=12.5$.

Answer:

$15\%$

10.