Math  /  Algebra

QuestionWhich expression is equivalent to 15(207y+10)?\frac{1}{5}(20-7 y+10) ?
Choose the correct answer below. A. 135y-\frac{13}{5} y B. 675y6-\frac{7}{5} y C. 135y\frac{13}{5} y D. 6+75y6+\frac{7}{5} y. Help me solve this View an example

Studdy Solution

STEP 1

1. We need to simplify the expression 15(207y+10)\frac{1}{5}(20-7y+10).
2. The expression can be simplified by distributing the 15\frac{1}{5} across each term inside the parentheses.

STEP 2

1. Distribute 15\frac{1}{5} to each term inside the parentheses.
2. Simplify the resulting expression.

STEP 3

Distribute 15\frac{1}{5} to each term in the expression 207y+1020 - 7y + 10:
15×2015×7y+15×10\frac{1}{5} \times 20 - \frac{1}{5} \times 7y + \frac{1}{5} \times 10

STEP 4

Calculate each term separately:
15×20=4\frac{1}{5} \times 20 = 4
15×7y=75y\frac{1}{5} \times 7y = \frac{7}{5}y
15×10=2\frac{1}{5} \times 10 = 2

STEP 5

Combine the simplified terms:
475y+24 - \frac{7}{5}y + 2
Combine the constant terms:
4+2=64 + 2 = 6
So the expression simplifies to:
675y6 - \frac{7}{5}y
The correct answer is:
B. 675y6 - \frac{7}{5} y

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