Download Forming and Solving Equations Worksheet

Forming and Solving Equations
Section A – unknown on one side
For each question you need to write out an equation (using ‘x’ or whatever letter you
want!) and solve it using the methods you’ve learnt.
a) I think of a number. I multiply it by 6 and add 3. If my answer is 75, calculate the
number I started with.
b) There are ‘b’ daffodil bulbs in a bag. I buy 4 bags, but 5 of the bulbs have gone bad
and will not grow. If I still have 55 bulbs that will grow, calculate the number of bulbs in
each bag.
c) The mean of 3 numbers is 12. If one number is 5 and the other is 11, write an equation
and solve it to find the third number. (Think about what you’d do with the numbers to
calculate the mean!)
d) The triangle to the right
is Isosceles. Calculate the lengths
of the sides if the perimeter
is 68cm.
2x - 1
x
Section B – unknown on both sides
a) Tom and Ellie both have the same amount of money to begin with. Tom multiplies his
by 4 and adds 50p. Ellie multiplies hers by 9 and subtracts £3. They end up with the
same amount of money. Calculate the amount they started with.
b) Alex thinks of a number. He adds 18 then divides it by 2. He gets the same answer
that he would have if he had multiplied the original number by 5. Calculate the mystery
number.
c) Rectangle A has one side which is 6cm long and the other is (x + 2)cm long. Rectangle
B has sides of length (2x + 1) and 3cm. If the perimeters are the same, calculate the
value of x and hence, the lengths of the sides of the rectangles.
d) Rectangle X measures 7cm by (x + 1)cm. Rectangle Y has dimensions of (3x + 6)cm and
4cm. The area of rectangle X is half the area of rectangle Y. Calculate the lengths of
the sides of the rectangles, and hence, their areas.
Super Challenge Question
Adam has sticks of the following lengths:
(3x + 4)cm
(2x + 10)cm
(x + 12)cm
He puts all 3 sticks together to make a triangle. The triangle is Isosceles. Calculate the
3 possible values of x.
Forming and Solving Equations
Section A
1) 12
2) 15
3) 20
4) x = 14, sides - 14, 27, 27
Section B
1) 70p
2) 2
3) x = 4, sides are 6 x 6 and 9 x 3
4) x = 5, sides are 6 x 7 and 4 x 21 so areas are 42 and 84
Super Challenge Question
2, 4, or 6