Final answer:
To solve the word problem, we convert the verbal statements into an equation, simplify and solve for the variable. The solution to the equation yields the number as 52.
Step-by-step explanation:
The student's question involves forming an equation from a word problem and solving for the unknown variable. The key is to translate the verbal description into a mathematical statement.
Let's break down the question:
"10 less than 5 times the value of a number" translates to 5n - 10.
"10 times the quantity of 12 more than 1/4 of the number" translates to 10*(1/4n + 12).
Now, we can set up the equation:
5n - 10 = 10*(1/4n + 12)
Solving this equation involves distributing the 10 on the right side, moving all terms to one side to set the equation to zero, and then solving for n.
- Multiply out the right side: 5n - 10 = 10/4n + 120
- Simplify the equation: 5n - 10 = 2.5n + 120
- Get all n terms on one side: 5n - 2.5n = 120 + 10
- Simplify and solve for n: 2.5n = 130
- Divide both sides by 2.5: n = 52
The number in question is 52.