Question

Tomas used 3 and one-third cups of flour and now has 1 and two-thirds cups left. Which equation can he use to find f, the number of cups of flour he had to begin with?
f + 3 and one-third = 1 and two-thirds
f minus 3 and one-third = 1 and two-thirds
3 and one-third f = 1 and two-thirds
f divided by 3 and one-third = 1 and two-thirds

Answer 1

To determine the number of cups of flour Tomas had to begin with, we need to set up an equation that incorporates both the amount he used and the amount he has left.

Let's break down the problem:

- Let \( f \) be the initial amount of flour Tomas had.
- He used \( 3 \frac{1}{3} \) cups of flour, so we can express this as \( \frac{10}{3} \) cups (since \( 3 \frac{1}{3} = 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3} \)).
- He has \( 1 \frac{2}{3} \) cups of flour left, which can be expressed as \( \frac{5}{3} \) cups (since \( 1 \frac{2}{3} = 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \)).

The relationship can be described by the equation:

\[
f - \frac{10}{3} = \frac{5}{3}
\]

To find \( f \), we can rearrange this equation as follows:

\[
f = \frac{10}{3} + \frac{5}{3}
\]

Thus, the correct equation based on the choices given is:

**f minus 3 and one-third = 1 and two-thirds.**

This corresponds to option 2:

\[
f - 3 \frac{1}{3} = 1 \frac{2}{3}
\]

So the answer is:

**f - 3 and one-third = 1 and two-thirds.**