Question

midterm review
warm up #2
translate and solve the following.

1. 8 more than a number is 5
2. the product of a number and 4 equals 20
3. 5 less than twice a number equals 25
4. the quotient of a number and -3 equals 6

solve the proportion.

1. \\(\frac{x + 3}{2} = \frac{10}{4}\\)
2. \\(-\frac{1}{3} = \frac{x + 4}{x}\\)
3. erica earns $45 for mowing 3 lawns. how much does she earn for 1 lawn?
4. the ratio of boys to girls in our class is 3 to 5. if there are 25 girls in the class, how many boys are there?

Explanation:

Problem 1: 8 more than a number is 5

Step1: Define the variable

Let the number be \( x \). "8 more than a number" translates to \( x + 8 \), and "is 5" means \( x + 8 = 5 \).

Step2: Solve for \( x \)

Subtract 8 from both sides: \( x = 5 - 8 \)
\( x = -3 \)

Step1: Define the variable

Let the number be \( x \). "The product of a number and 4" is \( 4x \), and "equals 20" gives \( 4x = 20 \).

Step2: Solve for \( x \)

Divide both sides by 4: \( x = \frac{20}{4} \)
\( x = 5 \)

Step1: Define the variable

Let the number be \( x \). "Twice a number" is \( 2x \), "5 less than twice a number" is \( 2x - 5 \), and "equals 25" gives \( 2x - 5 = 25 \).

Step2: Solve for \( x \)

Add 5 to both sides: \( 2x = 25 + 5 \)
\( 2x = 30 \)
Divide both sides by 2: \( x = \frac{30}{2} \)
\( x = 15 \)

Answer:

\( x = -3 \)

Problem 2: The product of a number and 4 equals 20