Certainly! Let's match each expression with the correct scenario step by step:
1. The price of a game that's been discounted [tex]\( 18\% \)[/tex] off its list price [tex]\( (x) \)[/tex]:
- When the price is discounted by [tex]\( 18\% \)[/tex], you are left with [tex]\( 82\% \)[/tex] of the original price. The expression for [tex]\( 82\% \)[/tex] of [tex]\( x \)[/tex] is [tex]\( 0.82 \cdot x \)[/tex]. Hence, the scenario matches with the expression [tex]\( 0.82 \cdot x \)[/tex].
2. The price of a toy that sells for [tex]\( 18\% \)[/tex] more than the amount [tex]\( (x) \)[/tex] needed to build the toy:
- If the toy sells for [tex]\( 18\% \)[/tex] more than the amount needed to build it, the total price is [tex]\( 118\% \)[/tex] of [tex]\( x \)[/tex]. The expression for [tex]\( 118\% \)[/tex] of [tex]\( x \)[/tex] is [tex]\( 1.18 \cdot x \)[/tex]. Therefore, this scenario matches with [tex]\( 1.18 \cdot x \)[/tex].
3. The volume of water remaining in a tank after [tex]\( \frac{3}{10} \)[/tex] of its original volume [tex]\( (x) \)[/tex] is drained out:
- When [tex]\( \frac{3}{10} \)[/tex] of the volume is drained, [tex]\( \frac{7}{10} \)[/tex] of the volume remains. Thus, [tex]\( \frac{7}{10} x \)[/tex] represents the remaining volume. This means the scenario matches the expression [tex]\( \frac{7}{10} x \)[/tex].
4. The total amount of flour in a bakery after receiving new stock equal to [tex]\( \frac{3}{10} \)[/tex] of its current stock [tex]\( (x) \)[/tex]:
- Receiving new stock equal to [tex]\( \frac{3}{10} \)[/tex] of the current stock means you have [tex]\( 1 + \frac{3}{10} = \frac{13}{10} \)[/tex] of the original amount. The expression for this is [tex]\( \frac{13}{10} x \)[/tex]. This scenario matches the expression [tex]\( \frac{13}{10} x \)[/tex].
Thus, the correct matches are:
- The price of a game that's been discounted [tex]\(18\% \)[/tex] off its list price [tex]\( (x) \)[/tex]: [tex]\( 0.82x \)[/tex]
- The price of a toy that sells for [tex]\(18\% \)[/tex] more than the amount [tex]\( (x) \)[/tex] needed to build the toy: [tex]\( 1.18x \)[/tex]
- The volume of water remaining in a tank after [tex]\( \frac{3}{10} \)[/tex] of its original volume [tex]\( (x) \)[/tex] is drained out: [tex]\( \frac{7}{10} x \)[/tex]
- The total amount of flour in a bakery after receiving new stock equal to [tex]\( \frac{3}{10} \)[/tex] of its current stock [tex]\( (x) \)[/tex]: [tex]\( \frac{13}{10} x \)[/tex]
