Question

Li uses 8.4 grams of sugar every day in her tea. Sue uses 12.6 grams of sugar every day in her coffee. If Li's sugar canister contains 128 grams of sugar and Sue's canister contains 191 grams, in how many days will Li and Sue have the same amount of sugar in their canisters?

Answer 1

To find out when Li and Sue will have the same amount of sugar in their canisters, we can set up equations based on the sugar they consume daily.

Let \( d \) represent the number of days.

For Li:
- Initial amount of sugar: \( 128 \) grams
- Daily consumption: \( 8.4 \) grams
- Amount of sugar in canister after \( d \) days:
\[
128 - 8.4d
\]

For Sue:
- Initial amount of sugar: \( 191 \) grams
- Daily consumption: \( 12.6 \) grams
- Amount of sugar in canister after \( d \) days:
\[
191 - 12.6d
\]

To find when both have the same amount of sugar in their canisters, we set the two equations equal to each other:
\[
128 - 8.4d = 191 - 12.6d
\]

Now, we simplify the equation.
First, add \( 12.6d \) to both sides:
\[
128 + 4.2d = 191
\]

Next, subtract \( 128 \) from both sides:
\[
4.2d = 191 - 128
\]
\[
4.2d = 63
\]

Now, divide by \( 4.2 \):
\[
d = \frac{63}{4.2}
\]

Perform the division:
\[
d = 15
\]

Thus, Li and Sue will have the same amount of sugar in their canisters in \( \boxed{15} \) days.