Question

write an algebraic expression for each verbal description.

1. half of the seventh graders and one third of the eighth graders were

divided into ten teams.

1. thirty percent of the green house flowers are added to 25 ferns for the

school garden.

1. four less than three times the number of egg orders and six more than

two times the number of waffle orders.

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Explanation:

Question 4

Step1: Define variables

Let \( s \) be the number of seventh graders and \( e \) be the number of eighth graders.

Step2: Find half of seventh graders and one third of eighth graders

Half of seventh graders is \( \frac{1}{2}s \), one third of eighth graders is \( \frac{1}{3}e \).

Step3: Divide the sum by 10

The sum of these two groups is \( \frac{1}{2}s+\frac{1}{3}e \), and dividing by 10 gives \( \frac{\frac{1}{2}s + \frac{1}{3}e}{10} \) (or we can simplify the fraction: \( \frac{3s + 2e}{6\times10}=\frac{3s + 2e}{60} \)).

Step1: Define variable

Let \( f \) be the number of greenhouse flowers.

Step2: Find thirty percent of greenhouse flowers

Thirty percent of \( f \) is \( 0.3f \) (or \( \frac{30}{100}f=\frac{3}{10}f \)).

Step3: Add 25 ferns

Adding 25 ferns to this group gives \( 0.3f + 25 \) (or \( \frac{3}{10}f+25 \)).

Step1: Define variables

Let \( e \) be the number of egg orders and \( w \) be the number of waffle orders.

Step2: Find three times the number of egg orders and four less than that

Three times the number of egg orders is \( 3e \), four less than that is \( 3e - 4 \).

Step3: Find two times the number of waffle orders and six more than that

Two times the number of waffle orders is \( 2w \), six more than that is \( 2w + 6 \).

Step4: Combine the two expressions

The expression for the combined quantity is \( (3e - 4)+(2w + 6) \), which simplifies to \( 3e+2w + 2 \) (by combining like terms: \( - 4+6 = 2 \)).

Answer:

\( \frac{\frac{1}{2}s+\frac{1}{3}e}{10} \) (or \( \frac{3s + 2e}{60} \))

Question 5