Pregunta
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
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The son is 7 years old.
Solución
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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Simplifique esta solución 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!
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