Question

1. which is equivalent to the equation below?

$\frac{n}{3} - 2 = 10$
a. two less than 3 times a number, n, is 10.
b. two minus 3 times a number, n, is 10.
c. two less than one - third of a number, n, is 10.
d. two minus one - third of a number, n, is 10.

1. mr. millers age is 3 years less than 4 times his sons age. mr. miller is 45 years old. the equation below represents this situation.

$4s - 3 = 45$
what does s represent in this situation?
a. the age of mr. miller
b. the age of mr. millers son
c. the sum of mr. millers age and his sons age
d. the difference between mr. millers age and his sons age

1. vincent was a given a gift card to a smoothie shop. each smoothie at the shop costs $4. the original balance on vincents card was $40. after buying several smoothies, he had $28 left on his card.

a. choose a variable to represent the unknown value in the situation. explain what the variable represents.

b. write an algebraic equation that could be used to find the unknown value in this situation.

Explanation:

Question 7

Step1: Analyze the equation $\frac{n}{3}-2 = 10$

The term $\frac{n}{3}$ means one - third of a number $n$, and then we subtract 2 from it (two less than one - third of $n$) and set it equal to 10.

Step2: Evaluate each option

• Option A: "Two less than 3 times a number, $n$, is 10" would be represented as $3n - 2=10$, not $\frac{n}{3}-2 = 10$. So A is incorrect.
• Option B: "Two minus 3 times a number, $n$, is 10" would be $2 - 3n=10$, which is not the given equation. So B is incorrect.
• Option C: "Two less than one - third of a number, $n$, is 10" matches the equation $\frac{n}{3}-2 = 10$.
• Option D: "Two minus one - third of a number, $n$, is 10" would be $2-\frac{n}{3}=10$, which is not the given equation. So D is incorrect.

The equation is $4s-3 = 45$, and the problem states that Mr. Miller's age is 3 years less than 4 times his son's age. Let's analyze each option:

• Option A: If $s$ was Mr. Miller's age, the equation would not be in the form of $4s - 3$ (since Mr. Miller's age is 45). So A is incorrect.
• Option B: If $s$ is the age of Mr. Miller's son, then 4 times his son's age is $4s$, and 3 years less than that is $4s - 3$, which equals Mr. Miller's age (45). This matches the situation.
• Option C: The sum of their ages would be $s + 45$, and the equation is not about the sum. So C is incorrect.
• Option D: The difference between their ages is $45 - s$, and the equation is not about the difference. So D is incorrect.

The unknown value in this situation is the number of smoothies Vincent bought. Let's choose the variable $x$ to represent the number of smoothies. The variable $x$ represents the number of smoothies Vincent purchased because we know the cost per smoothie, the initial balance, and the remaining balance, and the number of smoothies is what we need to find.

Answer:

C. Two less than one - third of a number, $n$, is 10.

Question 8