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# A bunch of Ratio problems

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A. The Specialty Soap Company can make 28 boxes of soap every 15 minutes using 4machines (at full speed). Because of a successful marketing campaign, they now needto make 280 boxes of soap every 30 minutes, and the company must now buy moremachines to handle the load. Assuming the production rate stays the same, howmany additional machines are needed?

B. Jill loves tiny animal figurines and has a collection of them. In her collection she has 2 bears for every 5 monkeys. She just had her birthday celebration and got 2 morebear figurines and 7 more monkey figurines. Now in her collection she has 3 bear sfor every 8 monkeys. How many figurines are there in her latest collection includingthe birthday gifts?

C. Winnie and her younger sister Vincy like to earn Junior Ranger batches whenever their family visited the National Parks. So far, for every 10 batches Winnie collected,Vincy had 7. Winnie decided to give Vincy 3 Junior Ranger batches (mostly duplicates that Vincy didn’t own). Vincy was thrilled, and after the exchange, for every 9 batches Winnie has in her collection, Vincy has 8.How many Junior Ranger batches do they have altogether?

D. Andrew asked his uncle and his grandpa how old they are. Uncle Joe smiled, “your grandpa is three times as old as I am”. Andrew complained, “there are many possibilities!” Grandpa laughed, “but 8 years ago, I was four times as old as your uncle was!” How old is grandpa now?

E. Ms. Elizabeth has a stash of gold and silver ribbons to reward well-behaved students. At the beginning of the year, she had 1 gold ribbon for every 2 silver ribbons. After giving out 10 gold ribbons and 32 silver ribbons, now the gold-to-silver ratio became 3:4. How many ribbons did Ms. Elizabeth start with at the beginning of the year?

F. It was raining outside and making a rhythmic dripping sound that slightly amused Samatha. She counted 6 drips every 20 seconds. It is 10:00pm at night. At this rate,how many drips will Samatha hear until midnight (counting the drips at 10:00pm and midnight)?

Jan 8, 2021

#1
+218
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A) The number of boxes were multiplied by 10 and the time by 2 so the number of machines must be multiplied by 10/2=5 meaning there are 16 additional machines.

B) We have two equations.5B=2M and 8(B+2)=3(M+7). Solving these gets us 12 bears and 32 monkeys so there are 44 total figurines.

C) 7W=10V and 8(W-3)=9(V+3). This gets us Winnie had 30 and Vincy 21. There are 51 total batches.

D) Lets set the uncle's age as U and the grandpa's as G. We are given 3U=G and 4(U-8)=G-8. Therefore U=24 and G=72. Grandpa is 72 years old.

E) Set gold ribbons as G and silver ones as S. We know that 2G=S and 4(G-10)=3(S-32) that gives us G=28 and S=56. Ms. Elizabeth started with 84 ribbons.

F) There are 6 drips every 20 seconds meaning there are 18 a minute. There are 121 minutes (including 10:00 and midnight) and 121*18=2178 so there are 2178 total drips.

:D

Jan 8, 2021

#1
+218
+1

A) The number of boxes were multiplied by 10 and the time by 2 so the number of machines must be multiplied by 10/2=5 meaning there are 16 additional machines.

B) We have two equations.5B=2M and 8(B+2)=3(M+7). Solving these gets us 12 bears and 32 monkeys so there are 44 total figurines.

C) 7W=10V and 8(W-3)=9(V+3). This gets us Winnie had 30 and Vincy 21. There are 51 total batches.

D) Lets set the uncle's age as U and the grandpa's as G. We are given 3U=G and 4(U-8)=G-8. Therefore U=24 and G=72. Grandpa is 72 years old.

E) Set gold ribbons as G and silver ones as S. We know that 2G=S and 4(G-10)=3(S-32) that gives us G=28 and S=56. Ms. Elizabeth started with 84 ribbons.

F) There are 6 drips every 20 seconds meaning there are 18 a minute. There are 121 minutes (including 10:00 and midnight) and 121*18=2178 so there are 2178 total drips.

:D

AvenJohn Jan 8, 2021
#2
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Thx for helping :)

Jan 8, 2021