I need to know how to write a pair of linear equations in two variables from a word problem

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Harry the Hungry Hippo is munching on the lily pads in his pond. When he got to the pond, there were 20 lily pads, but he is eating 4 lily pads an hour. Heinrick the Hungrier Hippo found a better pond with 29 lily pads! He eats 7 lily pads every hour.

  1. If Harry and Heinrick start eating at the same time, when will their ponds have the same number of lily pads remaining?

                b. How many lily pads will be left in each hole at that time?

Sangeetha Pulapaka

Step 1 : Identify the variables

Let x be the time and y be the number of lilies in the pond

Harry the hiippo is eating 4 lily pads an hour and there are 20 lily pads in the pond at present

So we write y = - 4x +20

Henricks pond has 29 lily pads and he is eating 7 lily pads in an hour

So we write y = -7x +29

Step 2: Recall on how to solve for an unknown variable  by using the substitution (easy) method


Solve for x

-4x + 20 = -7x +29

-4x +20 +7x = -7x +29 +7x

3x +20 = 29

3x +20 -20 = 29 - 20

3x = 9

x = 3

Therefore after 3 hours there will be the same number of lily pads in both the ponds.

Step 3: Substitute the known value in any of the linear equations to get the unknown value

Substituting x = 3 in y = 20 - 4x

y = 20 - 12 = 8

So there will be 8 lily pads left in each hole at the time.

Further skills you may want to recall:

What is a variable