To find out when the two machines will have the same amount of ice cream left, we can set up the following equations based on the initial capacities and daily sales:
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For the vanilla ice cream machine: \[ \text{Remaining vanilla} = 180 - 20x \] where \( x \) is the number of days.
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For the chocolate ice cream machine: \[ \text{Remaining chocolate} = 140 - 16x \]
To find when the amounts are equal, we set the two equations equal to each other: \[ 180 - 20x = 140 - 16x \]
Now, let's solve the equation step by step:
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Rearranging the equation, we can bring all the terms involving \( x \) to one side and the constant terms to the other: \[ 180 - 140 = 20x - 16x \] \[ 40 = 4x \]
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Now, divide both sides by 4 to solve for \( x \): \[ x = 10 \]
Thus, the solution is \( x = 10 \). This means that after 10 days, both machines will have the same amount of ice cream left.
The correct equation used is: \[ 180 - 20x = 140 - 16x \]
And the value of \( x \) is: \[ x = 10 \]
The responses "180−20x=140−16x ; x=10" and "180 minus 20 x equals 140 minus 16 x ; x equals 10" are both correct.