This morning’s Boston Globe had a story about the MCAS (Massachusetts Comprehensive Assessment System test. They quoted what was, going by the number of kids who got it wrong, the hardest question on the 10th grade math test.
Of the people in attendance at a recent baseball game, one-third had grandstand tickets, one-fourth had bleacher tickets, and the remaining 11,250 people in attendance had other tickets. What was the total number of people in attendance at the game?
Now, I freely admit I have a head for math. I can do arithmetic and algebra in my head faster (sometimes a LOT faster) than a lot of people can with a calculator. And it surprises me sometimes when others can’t, or seem surprised that I can. But this was NOT that tough a problem. I broke it down and had the answer in about 30-40 seconds, just in my head. But over half the tenth-graders in the Bay State blew it — and they had access to pencil, paper, and a calculator.
If we need more evidence that the public school system is failing our children, here it is.
(Solution in the extended section)
OK, we have 1/3 of X plus 1/4 of X equals X-11,250. First, make the fractions compatible (simplifying the denominator) by converting them to twelfths — 1/3 = 4/12, and 1/4 = 3/12.
That changes it to 4/12 X + 3/12 X = X – 11,250, which means that 7/12 = X – 11,250. And since X, in twelfths, is 12/12, we have 7/12 X = 12/12 X -11,250. Subtract 7/12 X from both sides, and we get that 0 = 5/12 X – 11,250. Then add 11,250 to both sides and you get 11,250 = 5/12 X.
Divide 11,250 by 5, and you find out that X = 2,250 (my shortcut here is instead of dividing it by five, I multiply it by 2 and then divide by ten. That gives me the answer 22,500, and then I just move the decimal place one place to the left and get 2,250. It’s faster for me.)
So, we now know that 1/12 of X is 2,250. So to get the final value of X, we multiply 2,250 by 12. But that can be tricky, so let’s do it in pieces.
You get 12 by multiplying 2 x 2 x 3. So let’s do this in steps. First, double 2,250 and get 4,500 — nice and simple. Then double it again and get 9,000 — also nice and simple. Finally, triple it, and you get the final answer — 27,000, or A.
It took me about five times as long to type this as it actually took me to think it through. Over half these kids, far better equipped and having had much more recent teaching on the subject, couldn’t do that.