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.