Problem Solving in Santa's Workshop
Clifford works in the gift-wrapping department of Santa's
workshop. His job is to finish all the packages with a bow.
He is running low on bows and only has 100 bows left. He
begins working at 5:00 a.m. During the first half-hour, he
uses 12 bows. In the second half-hour, he uses 9 bows.
During the third half-hour, he uses 14 bows and in the
fourth half-hour, he uses 11 bows. Clifford uses 16 bows
during the fifth half-hour. If the pattern continues, during
which half-hour will Clifford run out of bows?

Clifford uses 12 bows in the first half-hour, 9 bows in the second half-hour, 14 bows in the third half-hour, and 11 bows in the fourth half-hour, for a total of 12 + 9 + 14 + 11 = <<12+9+14+11=46>>46 bows used.

He has 100 bows and has used 46 bows, so he has 100 - 46 = <<100-46=54>>54 bows left.

If he uses 16 bows during the fifth half-hour, then he will have 54 - 16 = <<54-16=38>>38 bows left.

If he continues to use 16 bows per half-hour, then he will run out of bows during the 38 / 16 = <<38/16=2.375>>2.375 half-hours.

This means that Clifford will run out of bows at around the 2 and 3/8 half-hour mark, or around 2.375 * 30 minutes = <<2.375*30=71.25>>71.25 minutes into his shift.

Since a half-hour is 30 minutes, this means that Clifford will run out of bows at around 5:00 a.m. + 71.25 minutes = <<5+71.25=76.25>>76.25.

This means that Clifford will run out of bows during the 76.25 / 60 = <<76.25/60=1.27>>1.27 hours into his shift, or around the 1 and 1/4 hour mark.

Thus, Clifford will run out of bows during the sixth half-hour of his shift.

semsee45 semsee45 · Answer 2 · 2022-12-24T11:03:50+01:00

Answer:

Eighth half-hour

Step-by-step explanation:

Given pattern:

1st half hour = 12 bows used
2nd half hour = 9 bows used
3rd half hour = 14 bows used
4th half hour = 11 bows used
5th half hour = 16 bows used

Calculate the differences between the number of bows used:

[tex]12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16[/tex]

Therefore, the pattern for the bows used is:

-3, +5, -3, +5, etc...

If the pattern continues:

[tex]12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16\underbrace{}_{-3}13\underbrace{}_{+5}18\underbrace{}_{-3}15\underbrace{}_{+5}20[/tex]

6th half hour = 16 - 3 = 13 bows used
7th half hour = 13 + 5 = 18 bows used
8th half hour = 18 - 3 = 15 bows used
9th half hour = 15 + 5 = 20 bows used

Create a table with the given and found data, and add a cumulative total column:

[tex]\begin{array}{c|c|c}\vphantom{\dfrac12} \textsf{Half Hour} & \textsf{Bows used per half hour} & \sf Cumulative\; total\\\cline{1-3} \vphantom{\dfrac12} \sf 1st & 12 & 12\\\vphantom{\dfrac12} \sf 2nd &9 &21 \\\vphantom{\dfrac12} \sf 3rd & 14&35 \\\vphantom{\dfrac12} \sf 4th & 11& 46\\\vphantom{\dfrac12} \sf 5th & 16& 62\\\vphantom{\dfrac12} \sf 6th & 13& 75\\\vphantom{\dfrac12} \sf 7th &18 & 93\\\vphantom{\dfrac12} \sf 8th & 15& 108\\\vphantom{\dfrac12} \sf 9th & 20& 128\\\end{array}[/tex]

If Clifford has a total of 100 bows, he will run out of bows during the eighth half-hour.