Question
b) The sum of the age of a mother and three times the age of her son is 51 years. (i) Write an equation to represent the sum of the ages. \( n+3 y=51 \) (ii) If the mother is 30 years old, find the age of the son.
Ask by Patel Mccarthy. in Nepal
Nov 13,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The son is 7 years old.
Solution
To solve the problem, we start with the equation given in part (i):
\[
n + 3y = 51
\]
where \( n \) is the age of the mother and \( y \) is the age of the son.
In part (ii), we are given that the mother is 30 years old, so we can substitute \( n = 30 \) into the equation:
\[
30 + 3y = 51
\]
Now, we can solve for \( y \):
1. Subtract 30 from both sides:
\[
3y = 51 - 30
\]
\[
3y = 21
\]
2. Divide both sides by 3:
\[
y = \frac{21}{3}
\]
\[
y = 7
\]
Thus, the age of the son is \( 7 \) years old.
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Simplify this solution The Deep Dive
If the mother is 30 years old, we can substitute \(n\) with 30 in the equation \(n + 3y = 51\). So, we have: \[30 + 3y = 51\] Now, subtract 30 from both sides: \[3y = 51 - 30\] Which simplifies to: \[3y = 21\] Next, divide both sides by 3 to find the age of the son: \[y = \frac{21}{3} = 7\] Thus, the son is 7 years old! It's always fun to break down problems like these into bite-sized pieces. When tackling equations, remember to isolate the variable (in this case, \(y\)) and simplify step by step, just like following a recipe!
