Question

Larry sold twice as many magazines as Jan. Henry sold 8 more magazines than Jan did. Larry and Henry sold the same amount of magazines. How many magazines did Jan sell?

Show work

Answer 1

16 magazines jan sold

Answer 2

The magazines sold by Jan is 8

Solution:

Let us denote Larry by l, Jan by j and Henry by h.

We are given that Larry sold twice as many magazines as Jan.

So we can formulate an equation as follows;

l =2j --eq1

We also know that Henry sold 8 more magazines than Jan did.

Therefore it can be written as;

h=8+j --eq2

We have also been given that Larry and Henry sold the same amount of magazines.

This can be written as follows;

h = l --eq3

we can rewrite eq1 in term of l

`j=(l)/(2)` -- eqn 4

By substituting eq4 in eq2 we get;

`h = 8+ (l)/(2)`

`h = ((16+l))/(2)`

2h = 16 + l --eq5

From eq3 we know that h = l

Therefore by substituting h for l we can rewrite eq5 as;

2l = 16+l

l = 16

This implies Larry sold 16 magazines.

But we know that Larry sold twice as many magazines as Jan, therefore

`j = (16)/(2)`

j = 8

Hence Jan sold 8 magazines.