the sum of jack and jills ages is 84. if jill is twenty times hacks age, how old is each person

Question

equation and answer

Answer 1

So, we have a lot of information available in this question. We know that:

1. Jack's age + Jill's age = 84
2. Jill's age = 20 times Jack's age

Now, let's translate these statements in to mathematical ones. We'll make Jack's age in to the variable x, and Jill's age in to the variable y. So, now we have:

x + y = 84

y = 20x

Since the second statement defines the value of y, we can just take that value (20x) and plug it in to the first equation! So now we have:

x + 20x = 84

Now all we have to do is solve for x!

x + 20x = 84 (add the x variables)

21x = 84 (... then divide 84/21 to find x)

x = 21 (now we have Jack's age!)

So since we know Jack is 4 years old, we just have to plug it back in to the first equation and solve for y:

4 + y = 84 (move the numbers to one side and the variables to the other)

y = 84 - 4

y = 80 (now we have Jill's age!)

So now we know that Jack is 4, and Jill is 80! But let's double check if the values stay true in the second equation that the question gave us, which was y = 20x.

Is 80 = 20 x 4 true? Yes it is!