Substitution: Practice

How to use this set#

Ten ques­tions to solve by sub­sti­tu­tion. The first few are plain equa­tions; after that come word prob­lems, where you have to build the equa­tions your­self. For those, a small but pow­er­ful habit: write down what $x$ and $y$ stand for before you write any equa­tion, and give your final answer in the words of the ques­tion, with units. Exam­in­ers notice.

Sec­tion A, Equa­tions#

1. $x + y = 10$, $x - y = 4$.
2. $3x + y = 11$, $x + 2y = 7$.
3. $2x - 3y = 1$, $x + 4y = 6$.
4. $4x + 3y = 24$, $2x - y = 2$.
5. $\displaystyle \frac{x}{2} + y = 5$, $\displaystyle x - \frac{y}{3} = 3$.

Sec­tion B, Word prob­lems#

6. Two num­bers dif­fer by $5$, and twice the larger plus the smaller is $37$. Find the num­bers.
7. A father is $26$ years older than his daugh­ter. Six years from now, he will be three times as old as she will be. Find their present ages.
8. The cost of $2$ kg of apples and $1$ kg of grapes is ₹ $260$. The cost of $1$ kg of apples and $3$ kg of grapes is ₹ $330$. Find the cost per kg of each.
9. A two-digit num­ber has dig­its sum­ming to $11$. Revers­ing the dig­its gives a num­ber that is $27$ less than the orig­i­nal. Find the num­ber.
10. A frac­tion becomes $\displaystyle \frac{1}{2}$ when $1$ is added to its numer­a­tor, and becomes $\displaystyle \frac{1}{3}$ when $1$ is added to its denom­i­na­tor. Find the frac­tion.

Answers#