Question #2738e

The trick here is to realize that Anastasia's father is actually scaling up the number of items on the shopping list to #100#.

In other words, Anastasia's father is using a proportion to express the number of items the two already have on their list.

Notice that he says

We already have #60color(red)(%)# of the items on our list

Her father expresses the number of items they have in the shopping cart as a percentage. This sign

#color(red)(%)#

means out of #100#. You can thus say that the two have

#60color(red)(%) = "60 items" color(white)(.) color(red)("out of 100")#

in their shopping cart.

Now, Anastasia counted #12# items in the cart. This means that the #12# items they have in the cart would have been equal to #60# items if they would have had a total of #100# items on the list.

In other words, these #12# items represent the same proportion out of the total number of items as #60# items represent out of #100# items.

This is why I said that her father is using a proportion to tell her how many items they have in the cart.

#"12 items bought"/"total number of items" = "60 items bought"/"100 items"#

All you have to do now is cross multiply to find the number of items they have on the list

#"total number of items" = (12 color(red)(cancel(color(black)("items bought"))))/(60color(red)(cancel(color(black)("items bought")))) * "100 items"#

#color(darkgreen)(ul(color(black)("total number of items " = " 20 items")))#

Therefore, you can say that Anastasi and her father have #20# grocery items on their shopping list.