Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. match each expression to the scenario it represents. expressions: 1.18x, 18/10x, 0.82x, 3/10x, 7/10x, 0.18x scenarios: the price of a game that’s been discounted 18% off its list price (x); the price of a toy that sells for 18% more than the amount (x) needed to build the toy; the volume of water remaining in a tank after 3/10 of its original volume (x) is drained out; the total amount of flour in a bakery after receiving new stock equal to 3/10 of its current stock (x)

Explanation:

Step1: Analyze "18% off list price (x)"

A discount of 18% means we pay \(100\% - 18\% = 82\%\) of \(x\). \(82\% = 0.82\), so the expression is \(0.82x\).

Step2: Analyze "18% more than x"

18% more means \(100\% + 18\% = 118\%\) of \(x\). \(118\% = 1.18\), so the expression is \(1.18x\).

Step3: Analyze "After draining \(\frac{3}{10}\) of x"

Remaining volume is \(x-\frac{3}{10}x=\frac{10 - 3}{10}x=\frac{7}{10}x = 0.7x\)? Wait, no, \(\frac{7}{10}=0.7\)? Wait, no, \(\frac{7}{10}x\) is \(0.7x\)? Wait, no, the tiles have \(\frac{7}{10}x\) and \(\frac{3}{10}x\)? Wait, no, the tiles: \(\frac{3}{10}x\), \(\frac{7}{10}x\), etc. Wait, original volume \(x\), drain \(\frac{3}{10}x\), so remaining is \(x-\frac{3}{10}x=\frac{7}{10}x\).

Step4: Analyze "Receiving \(\frac{3}{10}\) of current stock (x)"

Total flour is \(x+\frac{3}{10}x=\frac{10 + 3}{10}x=\frac{13}{10}x = 1.3x\)? Wait, no, the tiles have \(\frac{13}{10}x\)? Wait, the tiles: \(1.18x\), \(\frac{13}{10}x\) (which is \(1.3x\)), \(0.82x\), \(\frac{3}{10}x\), \(\frac{7}{10}x\), \(0.18x\). Wait, let's re - check:

1. "18% off x": pay \(1 - 0.18=0.82\) of \(x\), so \(0.82x\).

1. "18% more than x": \(1 + 0.18 = 1.18\) of \(x\), so \(1.18x\).

1. "Drain \(\frac{3}{10}\) of x": remaining is \(x-\frac{3}{10}x=\frac{7}{10}x\).

1. "Receive \(\frac{3}{10}\) of x": total is \(x+\frac{3}{10}x=\frac{13}{10}x\) (since \(\frac{13}{10}=1.3\)? Wait, no, \(\frac{13}{10}x = 1.3x\)? Wait, the tile is \(\frac{13}{10}x\)? Wait, the tiles: \(\frac{13}{10}x\) is one of them? Wait, the given tiles are \(1.18x\), \(\frac{13}{10}x\) (which is \(1.3x\)), \(0.82x\), \(\frac{3}{10}x\), \(\frac{7}{10}x\), \(0.18x\).

So:

• "18% off x": \(0.82x\)

• "18% more than x": \(1.18x\)

• "After draining \(\frac{3}{10}x\)": \(x-\frac{3}{10}x=\frac{7}{10}x\)

• "After receiving \(\frac{3}{10}x\)": \(x+\frac{3}{10}x=\frac{13}{10}x\)

Answer:

• the price of a game that's been discounted 18% off its list price (\(x\)): \(0.82x\)

• the price of a toy that sells for 18% more than the amount (\(x\)) needed to build the toy: \(1.18x\)

• the volume of water remaining in a tank after \(\frac{3}{10}\) of its original volume (\(x\)) is drained out: \(\frac{7}{10}x\)

• the total amount of flour in a bakery after receiving new stock equal to \(\frac{3}{10}\) of its current stock (\(x\)): \(\frac{13}{10}x\)