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Question:

On the first day of the harvest, 186 boxes of oranges were collected. This is 29% less than what was collected on the second day. How many boxes were collected on the second day? (Round the answer to the nearest whole number)

A 262 boxes
explanation


Step 1: Establish a match
The expression “29% less than on the second day” means that 100% – 29% = 71% of the number of boxes collected on the second day were collected on the first day. Now, we know that 186 is 71% of the number that we are looking for. Let this number be x. We will set up an equation for x and solve it.
Step 2: Set up equalities
First of all, we will define the relationship between values and percentages:
100% = x
and
71% = 186
Step 3: Set up an equation
We will divide the second equation by first equation:
\( \frac{\mathrm{100\% } }{\mathrm{71 \% }} \)= \(\frac{\mathrm{x} }{\mathrm{186} }\)
Remember that you can perform the division only if the corresponding sides of the equations have the same units (e.g. percents must be divided by percents).
Step 4: Solve the equation for x
\(\frac{\mathrm{x} }{\mathrm{186} }\) = \(\frac{\mathrm{100} }{\mathrm{71} }\)
Finally, we will multiply both sides of the equation by 186:
\((\frac{\mathrm{x} }{\mathrm{186} }) × 186\) = \((\frac{\mathrm{100} }{\mathrm{71} }) × 186\)
Or, \(\frac{\mathrm{186x} }{\mathrm{186}} = \frac{\mathrm{18600} }{\mathrm{71} }\)
Or, x = 18600 ÷ 71
= 261.97
Since we are rounding to the nearest whole number, the answer is 262. Therefore, 262 boxes were collected on the second day.