Math

Question Find the value of xx where the ratios (3x+2):(2x+5)(3x+2):(2x+5) and 7:57:5 are equivalent. Provide the answer as an integer or simplified fraction.

Studdy Solution

STEP 1

Assumptions
1. We are given two equivalent ratios: (3x+2):(2x+5)(3x + 2):(2x + 5) and 7:57:5.
2. To find the value of xx, we need to set up a proportion and solve for xx.

STEP 2

Set up the proportion by equating the two ratios.
3x+22x+5=75\frac{3x + 2}{2x + 5} = \frac{7}{5}

STEP 3

Cross-multiply to eliminate the fractions and obtain a linear equation.
(3x+2)5=(2x+5)7(3x + 2) \cdot 5 = (2x + 5) \cdot 7

STEP 4

Distribute the numbers on both sides of the equation.
15x+10=14x+3515x + 10 = 14x + 35

STEP 5

Subtract 14x14x from both sides to get all terms with xx on one side.
15x14x+10=14x14x+3515x - 14x + 10 = 14x - 14x + 35

STEP 6

Simplify the equation by combining like terms.
x+10=35x + 10 = 35

STEP 7

Subtract 1010 from both sides to isolate xx.
x=3510x = 35 - 10

STEP 8

Calculate the value of xx.
x=25x = 25
The value of xx is 2525.

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