Question

sarah teaches craft classes. she has 214 bags of beads. each bag has enough beads for 22 bracelets. she estimates tht since 200 x 20 = 4000 there are enough beads for at least 4000 bracelets. tell how you can critique sarahs reasoning

Answer 1

Sarah estimated that she could make at least 4,000 bracelets from 214 bags of beads by simplifying the calculation to 200 bags with enough beads for 20 bracelets each. Her estimate was conservative, as the calculation of 214 bags multiplied by 22 bracelets per bag totals 4,708 bracelets, which is greater than her estimate.

Step-by-step explanation:

To critique Sarah's reasoning, we need to compare her estimate with the actual number of bracelets that can be made with the beads she has. She has 214 bags of beads, each with enough beads for 22 bracelets. To find the actual number of bracelets possible, we multiply the number of bags by the number of bracelets each bag can make:

214 bags × 22 bracelets per bag = 4,708 bracelets.

Sarah estimated that there were enough beads for at least 4,000 bracelets, based on the approximation that 200 bags with enough beads for 20 bracelets each would yield 4,000 bracelets. Although her estimation method simplifies the calculation by rounding down to manageable numbers, the actual total (4,708 bracelets) is greater than her estimate. By using this estimation method, Sarah has effectively ensured she will have more than enough beads for her classes, as her estimate is lower than the actual number.

Answer 2

Sarah's reasoning sounds good to start. She rounded the available bags and their content, so the result, 4000 bracelets, should be really easy to reach.

The exact numbers are 214 bags * 22 bracelets / bag = 4708 bracelets; so as you see, Sarah took care of having room to loose some beads and yet the beads will be enough to make 4000 bracelets.

Of course, if you want to be sure, you should ask Sarah some questions. For example:

1) What proportion of beads are normally deffective?

2) What proportion of beads are normally lost when crafting?

So, if Sarah did not take into account those proportions she migth be overestimating the number of bracelets they can make.