Gerald had a number of magazines and storybooks for sale. 40% of them were magazines and the rest were storybooks, When some magazines were sold, 15% of the total number of magazines and storybooks left were magazines. A total of 360 magazines and storybooks were left. How many magazines were sold?
total number of items for sale ---- 10x
number of mags = 4x
number of books = 6x
number of mags sold --- y
number of mags left = 4x - y
total left = 4x-y + 6x = 10x - y = 360
.15(10x - y) = 4x-y
solving this I got x = 51 and y = 150
put it all together.
Let x be the total number of magazines and storybooks that Gerald had.
Let y be the number of magazines that Gerald had.
Let z be the number of magazines that were sold.
From the problem statement, we know that 40% of the total number of magazines and storybooks were magazines. This means that:
y = 0.4x
We also know that after some magazines were sold, 15% of the total number of magazines and storybooks left were magazines. This means that:
(y - z) = 0.15(x - z)
Finally, we know that there were a total of 360 magazines and storybooks left. This means that:
x - z = 360
Now we have three equations with three unknowns. We can solve for them using substitution or elimination.
Substituting y = 0.4x into the second equation, we get:
(0.4x - z) = 0.15(x - z)
0.25x = 0.85z
z = (0.25/0.85)x
Substituting z = (0.25/0.85)x into the third equation, we get:
x - (0.25/0.85)x = 360
(0.6/0.85)x = 360
x = (360*0.85)/0.6
x = 510
Therefore, Gerald had a total of 510 magazines and storybooks.
To find out how many magazines were sold, we can substitute x and z into one of the previous equations:
(y - z) = 0.15(x - z)
(0.4*510 - z) = 0.15(510 - z)
204 - z = 76.5 - 0.15z
0.85z = 127.5
z = 150
Therefore, Gerald sold 150 magazines.