The larger of two numbers is 23. if three times the number is 5 more than eight times the smaller, find the smaller number.
Many students have difficulty translating an inequation into an equation.
Sometimes it helps to rephrase the statement into something like ...
"three times the number is more than 8 times the smaller by 5"
3(23) > 8x by 5
so add 5 to the smaller side and it becomes an "equation"
3(23) = 8x+5
69-5 = 8x
x = 8
the smaller number is 8
Let's assume the larger number is represented by x and the smaller number is represented by y.
Given:
The larger number (x) = 23
Three times the larger number (3x) is 5 more than eight times the smaller number (8y).
So, we can write the equation as:
3x = 8y + 5
Now, we need to solve this equation to find the value of the smaller number (y).
Substituting the value of x from the given information (x = 23) into the equation:
3(23) = 8y + 5
Simplifying:
69 = 8y + 5
Now we can isolate the term with y:
8y = 69 - 5
Simplifying further:
8y = 64
Finally, divide both sides by 8 to solve for y:
y = 64/8
y = 8
Therefore, the smaller number is 8.
To find the smaller number, let's assume the smaller number as "x". According to the given information, we know that the larger number is 23.
Now, we are given that "three times the number" (which is 3x) is "5 more than eight times the smaller" (which is 8x + 5).
Using this information, we can set up an equation:
3x = 8x + 5
To solve this equation, we need to isolate the variable "x" on one side. Let's do that step by step:
1. Subtract 8x from both sides:
3x - 8x = 8x + 5 - 8x
This simplifies to:
-5x = 5
2. Divide both sides by -5 to solve for x:
-5x / -5 = 5 / -5
This simplifies to:
x = -1
Hence, the smaller number is -1.