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QuestionFind the smaller number if the difference between two numbers is 8 and 3×smaller=greater+263 \times \text{smaller} = \text{greater} + 26.

Studdy Solution

STEP 1

Assumptions1. Let's denote the smaller number as x. . Let's denote the larger number as y.
3. We know that the difference between the two numbers is8, which can be written as y - x =8.
4. We also know that three times the smaller number is26 more than the larger number, which can be written as3x = y +26.

STEP 2

First, we need to express one of the variables in terms of the other. From the first equation, we can express y in terms of x.
y=x+8y = x +8

STEP 3

Now, substitute the expression for y from the first equation into the second equation.
3x=(x+8)+263x = (x +8) +26

STEP 4

implify the equation.
3x=x+343x = x +34

STEP 5

Subtract x from both sides of the equation to isolate the variable x.
3x−x=x+34−x3x - x = x +34 - x

STEP 6

implify the equation.
2x=342x =34

STEP 7

Divide both sides of the equation by2 to solve for x.
x=34/2x =34 /2

STEP 8

Calculate the value of x.
x=34/2=17x =34 /2 =17So, the smaller number is17.

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