Question: Alexander draws 9 pictures for an exhibition at a gallery. 5 new galleries also want Alexander to draw for them, so he draws pictures for their exhibitions too. Each of these new galleries receives the same amount of pictures. For each picture, Alexander needs 4 pencils. For each exhibition, he needs another 2 pencils for signing his signature on the pictures. If Alexander uses 88 pencils on drawing and signing his pictures for all of the exhibitions, how many paintings are at each of the 5 new galleries? Think carefully first, then make a decision:
Alexander has sent pictures to a total of 1 original gallery + 5 new galleries = 6 galleries. For signatures, he has used a total of 6 galleries * 2 pencils per gallery = 12 pencils. So of the pencils that he used, 88 total pencils – 12 signature pencils = 76 pencils for drawings. At the first gallery, he used 9 pictures * 4 pencils per picture = 36 pencils. So in the new galleries, he used 76 total pencils for drawings – 36 pencils at the first gallery = 40 pencils. The new galleries received a total of 40 pencils / 4 pencils per picture = 10 pictures. As the new galleries all receive equal amounts of pictures, each gallery must have 10 pictures / 5 galleries = 2 pictures per gallery. So the answer is 2.