I was using ChatGPT (with GPT 4) to solve this AMC 12 math problem. It sets up the equations correctly, but fails with some arithmetic at the very end: just adding fractions!
Somehow it simplifies 2(29/10) as 58/5 instead of 29/5.
I prompted it again pointing out that it calculated incorrectly, but still makes a similar arithmetic mistake. Any ideas or way to prompt ChatGPT to do arithmetic correctly?
Initial prompt
The roots of the polynomial 10x^3 - 39x^2 + 29x - 6 are the height, length, and width of a rectangular box (right rectangular prism). A new rectangular box is formed by lengthening each edge of the original box by 2 units. What is the volume of the new box?
Response
Let the roots of the polynomial be h, l, and w, which represent the height, length, and width of the original box, respectively. According to Vieta’s formulas, we can derive the following relationships from the polynomial’s coefficients:
h + l + w = 39/10
hl + hw + lw = 29/10
hlw = 6/10 = 3/5
Now, consider the new box with dimensions (h+2), (l+2), and (w+2). We want to find the volume of this new box, which is:
V_new = (h+2)(l+2)(w+2)
To find V_new, we can expand the expression:
V_new = (h+2)(l+2)(w+2)
= (hlw + 2lw + 2hw + 2hl + 4w + 4l + 4h + 8)
We know that h + l + w = 39/10, hl + hw + lw = 29/10, and hlw = 3/5, so we can substitute these values into the expression for V_new:
V_new = (3/5 + 2(29/10) + 4(39/10) + 8)
Now, we simplify the expression:
V_new = (3/5 + 58/5 + 156/5 + 8)
= (3/5 + 58/5 + 156/5 + 40/5)
= (3 + 58 + 156 + 40)/5
= 257/5
Thus, the volume of the new box is 257/5 cubic units.