The greater of two numbers is 1 less than three times the smaller. If 3 times the greater is 5 more than 8 times the smaller, find the number.
Let the smaller number be S, the greater number be G.
"The greater of two numbers is 1 less than three times the smaller"
G=3S-1 ......(1)
"3 times the greater is 5 more than 8 times the smaller"
3G=8S+5 .......(2)
Solve for G and S.
Try this.
Let x = smaller number
and y = greater number
=============================
3x-1=y
3y=8x+5
solve for x and y.
Let's solve this problem step by step.
Step 1: Identify the unknowns:
Let's assume that the smaller number is represented by "x" and the greater number is represented by "y".
Step 2: Translate the given information into equations:
From the problem, we can translate the first statement into an equation:
The greater of two numbers is 1 less than three times the smaller.
y = 3x - 1
Similarly, we can translate the second statement into an equation:
If 3 times the greater is 5 more than 8 times the smaller.
3y = 8x + 5
Step 3: Solve the equations:
Now, we have a system of two equations with two unknowns:
Equation 1: y = 3x - 1
Equation 2: 3y = 8x + 5
To solve these equations simultaneously, we can substitute the value of "y" from Equation 1 into Equation 2:
3(3x - 1) = 8x + 5
9x - 3 = 8x + 5
9x - 8x = 5 + 3
x = 8
Step 4: Substitute the value of x back into one of the original equations to find y:
Using Equation 1: y = 3x - 1
y = 3(8) - 1
y = 24 - 1
y = 23
Therefore, the smaller number is 8 and the greater number is 23.