Bat Cost
Just give me your instant, reflexive reaction as to what you think that the answer to the question is.
A ball and bat cost $1.10. The bat costs $1 more than the ball. How much does the ball cost?
If you're like most people, your immediate answer was, "Ten cents." And you'd be wrong.
Check it out. The bat costs $1 more than the ball. So if the ball costs ten cents, then the bat costs $1.10, and the total cost would be $1.20. That's too much.
We could try something lower. How about seven cents? Then the bat would cost $1.07, and the total would be $1.14. Closer, but still too high.
How about five cents? Then the bat would cost $1.05, and the total would be $1.10. So five cents is the right answer to the question of how much the ball costs. …show more content…
We could have noodled it out.
The total cost is $1.10. The price differential is $1. That leaves ten cents to be divided between the ball and the bat.
To maintain the price differential, this remainder has to be split evenly between the ball and the bat. So the ball costs five cents, and the other five cents is added to the differential to give the bat price of $1.05.
But we don't even have to noodle it out. We've developed techniques for solving problems such as this ball and bat problem, and by applying these techniques, we can automatically grind out the correct answer to the question. In the case of the ball and bat problem, the appropriate technique is algebra.
Here the unknown is the price of the ball, which we traditionally represent as "x". The price of the bat is then $1 more than the price of the ball, or "x + 1". If we add these two prices together, "x" + "x + 1", we get a total of $1.10.
A ball and bat cost $1.10. The bat costs $1 more than the ball. How much does the ball cost?
If you're like most people, your immediate answer was, "Ten cents." And you'd be wrong.
Check it out. The bat costs $1 more than the ball. So if the ball costs ten cents, then the bat costs $1.10, and the total cost would be $1.20. That's too much.
We could try something lower. How about seven cents? Then the bat would cost $1.07, and the total would be $1.14. Closer, but still too high.
How about five cents? Then the bat would cost $1.05, and the total would be $1.10. So five cents is the right answer to the question of how much the ball costs. …show more content…
We could have noodled it out.
The total cost is $1.10. The price differential is $1. That leaves ten cents to be divided between the ball and the bat.
To maintain the price differential, this remainder has to be split evenly between the ball and the bat. So the ball costs five cents, and the other five cents is added to the differential to give the bat price of $1.05.
But we don't even have to noodle it out. We've developed techniques for solving problems such as this ball and bat problem, and by applying these techniques, we can automatically grind out the correct answer to the question. In the case of the ball and bat problem, the appropriate technique is algebra.
Here the unknown is the price of the ball, which we traditionally represent as "x". The price of the bat is then $1 more than the price of the ball, or "x + 1". If we add these two prices together, "x" + "x + 1", we get a total of $1.10.