Studdy AI Logo
Math

QuestionMrs. Sanchez rounds rulers to the nearest 10 and sharpeners to 100. Why won’t this strategy work? What should she do?

Studdy Solution

STEP 1

Assumptions1. The number of supply kits needed for4th grade is134. The number of supply kits needed for5th grade is1433. The number of rulers ordered for4th grade is1304. The number of rulers ordered for5th grade is1405. The number of pencil sharpeners ordered for4th grade is1006. The number of pencil sharpeners ordered for5th grade is1007. Mrs. Sanchez rounds the number of rulers to the nearest10 and the number of pencil sharpeners to the nearest1008. Mrs. Sanchez orders rulers in packs of10 and pencil sharpeners in packs of100

STEP 2

First, let's analyze why Mrs. Sanchez's rounding strategy did not work. The problem arises when the number of supply kits needed is not exactly divisible by the pack size. For example, if we need134 rulers but they come in packs of10, rounding down to130 will not be enough. Similarly, if we need143 pencil sharpeners but they come in packs of100, rounding down to100 will not be enough.

STEP 3

To ensure that Mrs. Sanchez orders enough supplies, she should round up to the nearest pack size instead of rounding down. This means if the number of supplies needed is not exactly divisible by the pack size, she should order one more pack.

STEP 4

For the4th grade, she needs134 rulers, but they come in packs of10. So, she should round up to the nearest10.
Rulers for4th grade=⌈134/10⌉×10\text{Rulers for4th grade} = \lceil134/10 \rceil \times10

STEP 5

Calculate the number of rulers for the4th grade.
Rulers for4th grade=⌈13.4⌉×10=140\text{Rulers for4th grade} = \lceil13.4 \rceil \times10 =140

STEP 6

For the4th grade, she needs134 pencil sharpeners, but they come in packs of100. So, she should round up to the nearest100.
encil sharpeners for4th grade=⌈134/100⌉×100\text{encil sharpeners for4th grade} = \lceil134/100 \rceil \times100

STEP 7

Calculate the number of pencil sharpeners for the4th grade.
encil sharpeners for4th grade=⌈1.34⌉×100=200\text{encil sharpeners for4th grade} = \lceil1.34 \rceil \times100 =200

STEP 8

For the5th grade, she needs143 rulers, but they come in packs of10. So, she should round up to the nearest10.
Rulers for5th grade=⌈143/10⌉×10\text{Rulers for5th grade} = \lceil143/10 \rceil \times10

STEP 9

Calculate the number of rulers for the5th grade.
Rulers for5th grade=⌈14.3⌉×=150\text{Rulers for5th grade} = \lceil14.3 \rceil \times =150

STEP 10

For the5th grade, she needs143 pencil sharpeners, but they come in packs of100. So, she should round up to the nearest100.
encil sharpeners for5th grade=⌈143/100⌉×100\text{encil sharpeners for5th grade} = \lceil143/100 \rceil \times100

STEP 11

Calculate the number of pencil sharpeners for the5th grade.
encil sharpeners for5th grade=⌈.43⌉×100=200\text{encil sharpeners for5th grade} = \lceil.43 \rceil \times100 =200So, Mrs. Sanchez should order140 rulers and200 pencil sharpeners for the4th grade, and150 rulers and200 pencil sharpeners for the5th grade.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord