EQUATIONS- GRADE 10

EQUATIONS

GRADE 10

Solving simple equations

The trial and error method.

Twelve is divided by two numbers of which the value of one number is double that of the other. The difference between the two quotients is 2. Find the two numbers.

Case I: Can the two numbers be 2 and 4?
 $\frac{12}{2}=6\ and\ \frac{12}{4}=3$   so the difference is 6 – 3 = 3, and they do not work
Case II: Can the two numbers be 6 and 12?
 $\frac{12}{6}=2\ and\ \ \frac{12}{12}=1$  so the difference is 2 – 1 = 1, and they do not work.
Case III: Can the two numbers be 3 and 6?

 $\frac{12}{3}=4\ and\ \frac{12}{6}=2$  so the difference is 4 – 2 = 2, and they work!

Open Ended

Several friends shared 60 mangoes equally. One of them, Amal, sold three of his mangoes, and then he had only two mangoes left. How many friends shared the mangoes?

Open Ended

A father and his sons equally shared an amount of Rs 270. Then the amount each person had was Rs 45. Taking the number of sons as x, construct an equation. Solve this equation and hence find the number of sons the father has.

Open Ended

When the same number was added both to the numerator and the denominator of the fraction  $\frac{3}{5}$   , the resulting fraction was equal to   $\frac{9}{10}$   What number was added?

Simultaneous Equations

Sajithi and Sanjana have certain amounts of money. When twice the amount of money Sanjana has is added to the amount of money Sajithi has, we get Rs. 110. When thrice the amount of money Sanjana has is added to twice the amount of money Sajithi has, the amount is Rs. 190. Find the amount of money each has.

 $2m+3n=133$  

 $m+5n=21$  

 $x=3y$  

 $2x+3y=18$  

 $3x-4y=8\left(2-y\right)+1$  

 $2\left(2x+3y\right)=26-y$  

Open Ended

The price of two oranges and one king coconut is Rs. 80. Three king coconuts cost the same amount as two oranges. Find the price of an orange and a king coconut separately.

Open Ended

The price of two baby shirts and three pairs of baby shorts is Rs. 1150. Three baby shirts and a pairs of baby shorts cost Rs. 850. Taking the price of a baby shirt as Rs. x and that of a pairs of baby shorts as Rs. y, construct two simultaneous equations and find the price of a baby shirt and that of a pairs of baby shorts separately by solving the two equations.

Open Ended

Dinithi’s father tells Dinithi, “My age is now four times your age. 8 years earlier, I was twelve times older than you.” Find the present ages of the father and Dinithi separately.

Quadratic Equations

 $x^2+5x+6=0$   $2x^2-5x=0$   $x^2-9=0$  

                            $x^2+2x=0$  

                    $x^2-3x+2=0$  

                 $x^2-4x+-21=0$  

For you to think ...

• Where we can use simple, simultaneous, quadratic equations in our day to day life?

• What is the graphical representation of a function?