Respuesta :
Answer:
The number is 7.
[tex]x=7[/tex]Explanation:
Let us convert the sentences to a maths equation;
Let x represent the number.
"Eight times the result of subtracting 3 from a number"
[tex]8(x-3)[/tex]"the number increased by 25"
[tex]x+25[/tex]Since they are equal to each other, we have;
[tex]8(x-3)=x+25[/tex]Let's now solve the resulting equation;
[tex]\begin{gathered} 8(x-3)=x+25 \\ 8(x)+8(-3)=x+25 \\ 8x-24=x+25 \\ \text{add 24 to both sides} \\ 8x-24+24=x+25+24 \\ 8x=x+49 \\ \text{subtract x from both sides;} \\ 8x-x=x-x+49 \\ 7x=49 \\ \text{divide both sides by 7} \\ \frac{7x}{7}=\frac{49}{7} \\ x=7 \end{gathered}[/tex]Therefore, the number is 7.
[tex]x=7[/tex]
