For each problem, set up an equation and solve it using the balance method.

Question

For each problem, set up an equation and solve it using the balance method.

a) the perimeter of a rectangular car park is 88 m. If the length is 12m more than the width, what are the dimensions of the car park?

b) Lisa, Nicole and Tania scored a total of 29 goals in a netball match. Lisa scores five more goals than Nicole, and Tania scored three less than Nicole. How many goals did each girl score?

P.S. I know how to solve the questions but I don’t know how to set it up as an equation.

Answer 1

a) Perimeter of rectangle: P = 2 * (Length + width)

"The length if 12 more than the width" which means Length = Width +12

--> P = 2 * [(w +12) + w]

--> 88= 2 * ( 2w + 12)

--> 88= 4w + 24

--> 64= 4w

--> w= 16

Length = 16 +12 = 28 m

Width = 16 m

b) Lisa score five more goal than Nicole which means Lisa's scores= Nicole's scores + 5

Tania score three less than Nicole which means Tania's scores= Nicole's scores - 3

Total goals = Lisa + Nicole + Tania

--> 29= (N+5) + N + ( N - 3)

--> 29= 3N + (5 - 3)

--> 29= 3N - 2

--> 27= 3N

--> N = 9

Lisa = N +5 = 9 +5= 14 scores

Tania = N - 3 = 9 -3= 6 scores

Nicole = 9 scores