# Question 2738e

Feb 2, 2017

$20$

#### Explanation:

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.

$\text{12 items bought"/"total number of items" = "60 items bought"/"100 items}$

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

$\text{total number of items" = (12 color(red)(cancel(color(black)("items bought"))))/(60color(red)(cancel(color(black)("items bought")))) * "100 items}$

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{total number of items " = " 20 items}}}}$

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