Is it possible to answer this question with a double set matrix? I like the solution that is given, but I'd like to see how this can be solved with the matrix as well
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350 students at High School High are currently enrolled in French, Spanish, or both French and Spanish. 230 students are currently enrolled in Spanish.
In the table, identify the number of students currently enrolled in French and the number of students currently enrolled in both French and Spanish. The two numbers must be consistent with each other and with the constraints above. Make exactly one choice in each column.
French French and Spanish Number
140
180
200
220
260
280
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- connieyip11
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Re: Overlapping Set IR question
You can use the matrix. It's difficult to format the matrix on the forum, so I'll just describe it:
* Rows are French / not French / total; columns are Spanish / not Spanish / total. (As usual, rows and columns are interchangeable.)
* Bottom right corner = 350.
* Middle square = 0 (since everybody takes at least one of those languages).
* Top right corner ("Spanish, total") = 230.
* Subtract the right-hand column, giving the cell on the middle right ("Not Spanish, total") = 120.
* Subtract 120 minus 0 in the middle row, giving the middle left cell ("French, not Spanish") = 120.
From here, there are two options.
Algebra:
Put "x" in the top left box (French+Spanish).
Adding the left-hand column gives the lower left box (French, total) = x + 120.
There's no point in filling out the rest of the grid, because we now have expressions for the two quantities that we actually care about ("French+Spanish" and "French, total"), which are x and (x + 120) respectively.
therefore, these quantities have to be numbers that are exactly 120 apart.
the only choices here that do that are 140 and 260, so, there it is.
Plugging Numbers:
Pick a number from the answer choices, and plug it into either of the two desired boxes. (It's best to start with a bigger number if you plug in for "French, total", or a smaller number if you plug in for "French+Spanish".)
If you plugged in for "French+Spanish", then add 120, and see whether the resulting number is also a choice. (It won't be unless you picked 140.)
If you plugged in for "French, total", then subtract 120, and see whether the resulting number is also a choice. (It won't be unless you picked 260.)
* Rows are French / not French / total; columns are Spanish / not Spanish / total. (As usual, rows and columns are interchangeable.)
* Bottom right corner = 350.
* Middle square = 0 (since everybody takes at least one of those languages).
* Top right corner ("Spanish, total") = 230.
* Subtract the right-hand column, giving the cell on the middle right ("Not Spanish, total") = 120.
* Subtract 120 minus 0 in the middle row, giving the middle left cell ("French, not Spanish") = 120.
From here, there are two options.
Algebra:
Put "x" in the top left box (French+Spanish).
Adding the left-hand column gives the lower left box (French, total) = x + 120.
There's no point in filling out the rest of the grid, because we now have expressions for the two quantities that we actually care about ("French+Spanish" and "French, total"), which are x and (x + 120) respectively.
therefore, these quantities have to be numbers that are exactly 120 apart.
the only choices here that do that are 140 and 260, so, there it is.
Plugging Numbers:
Pick a number from the answer choices, and plug it into either of the two desired boxes. (It's best to start with a bigger number if you plug in for "French, total", or a smaller number if you plug in for "French+Spanish".)
If you plugged in for "French+Spanish", then add 120, and see whether the resulting number is also a choice. (It won't be unless you picked 140.)
If you plugged in for "French, total", then subtract 120, and see whether the resulting number is also a choice. (It won't be unless you picked 260.)
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