Question

Two equations are shown: • Equation 1: 3 4 (x−12)=12 •Equation 2: 3 4 y−12=12 Solve each equation. Then, enter a number in each box to make this statement true. The value of x is: The value of y is:

Answer 1

Answer:

The required value of x = 28

The required value of y = 32

Step-by-step explanation:

The given two equations are :

$\frac{3}{4}(x-12)=12..........(1)\\\\\frac{3}{4}\cdot y-12=12...........(2)$

Now, we need to solve both the equations and find out the required values of both the unknowns x and y.

Solving equation (1) to obtain value of x. We have,

$\frac{3}{4}(x-12)=12\\\\\text{On cross multiplication, we get}\\\\\implies 3\times (x-12)=12\times 4\\\implies 3x -36=48\\\implies 3x=48+36\\\implies 3x=84\\\bf\implies x=28$

Solving equation (2) to obtain value of y. We have,

$\frac{3}{4}\cdot y-12=12\\\\\implies \frac{3}{4}\cdot y=12+12\\\\\implies \frac{3}{4}\cdot y=24\\\\\text{On cross multiplicatrion, We get}\\\implies 3\cdot y=24\times 4\\\implies 3y = 96\\\bf\implies y=32$

Hence, The required value of x = 28

And The value of y = 32

Answer 2

Answer

$x=28$

$y=32$

Explanation

Let's solve each equation step by step

Equation 1: $\frac{3}{4} (x-12)=12$

Step 1. Distribute $\frac{3}{4}$

$\frac{3}{4} x-\frac{3}{4} *12=12$

$\frac{3}{4} x-9=12$

Step 2. Add 9 to both sides

$\frac{3}{4} x-9+9=12+9$

$\frac{3}{4} x=21$

Step 3. Multiply both sides of the equation by $\frac{4}{3}$

$\frac{3}{4} x*\frac{4}{3}=21*\frac{4}{3}$

$x=28$

Equation 2: $\frac{3}{4} y-12=12$

Step 1. Add 12 to both sides

$\frac{3}{4} y-12+12=12+12$

$\frac{3}{4} y=24$

Step 2. Multiply both sides by $\frac{4}{3}$

$\frac{3}{4} y*\frac{4}{3}= 24*\frac{4}{3}$

$y=32$