1. Let Rene's current age be \( R \) and her sister's current age be \( S \).
Given:
\( R = S + 6 \) (Rene is 6 years older)
After 10 years:
\( (R + 10) + (S + 10) = 50 \)
Substitute \( R = S + 6 \):
\( (S + 6 + 10) + (S + 10) = 50 \)
\( 2S + 26 = 50 \)
\( 2S = 24 \)
\( S = 12 \)
\( R = 12 + 6 = 18 \)
Answer: Rene is 18 years old, sister is 12 years old.
2. Let breadth be \( B \) meters.
Length = \( B + 10 \) meters.
Perimeter = \( 2 \times (B + B + 10) = 80 \)
\( 2 \times (2B + 10) = 80 \)
\( 4B + 20 = 80 \)
\( 4B = 60 \)
\( B = 15 \)
Length = \( 15 + 10 = 25 \)
Answer: Breadth is 15 m, Length is 25 m.
3. Let width be \( W \) meters.
Length = \( 2W \) meters.
Perimeter = \( 2 \times (W + 2W) = 300 \)
\( 2 \times (3W) = 300 \)
\( 6W = 300 \)
\( W = 50 \)
Length = \( 2 \times 50 = 100 \)
Answer: Breadth is 50 m, Length is 100 m.
4. Let my age be \( M \) years.
Mother's age = \( 2M + 12 \)
After 8 years:
Mother's age = \( 3M - 20 \)
So:
\( 2M + 12 + 8 = 3M - 20 \)
\( 2M + 20 = 3M - 20 \)
\( 40 = M \)
My age = 40 years
Mother's age = \( 2 \times 40 + 12 = 92 \) years
Answer: My age is 40 years, Mother's age is 92 years.
5. Let number of girls be \( G \).
Number of boys = \( \frac{2}{5}G \)
Total students = \( G + \frac{2}{5}G = 42 \)
\( \frac{7}{5}G = 42 \)
\( G = 42 \times \frac{5}{7} = 30 \)
Boys = \( \frac{2}{5} \times 30 = 12 \)
Answer: Boys = 12, Girls = 30.
Parent Tip: Review the logic above to help your child master the concept of linear equation word problems worksheet with answers.
