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defon
3 years ago
13

A group of ladies meet for an afternoon tea party. They bring all their cats. In all, there are 26 heads and 84 feet. How many l

adies and how many cats are in the room
Mathematics
2 answers:
SSSSS [86.1K]3 years ago
7 0
H=p+c  (heads equals the sum of people and cats) since there are 26 heads:

p+c=26, solve for c, subtract p from both sides

c=26-p, now for feet...

2p+4c=f, using c found above gives you:

2p+4(26-p)=f and we are told that there are 84 feet so:

2p+4(26-p)=84  perform indicated multiplication on left side

2p+104-4p=84, combine like terms on left side

-2p+104=84  subtract 104 from both sides

-2p=-20  divide both sides by -2

p=10, and since c=26-p

c=26-10

c=16

So there are 10 people and 16 cats in the room.


Komok [63]3 years ago
6 0




X= ladies       y = number of cats 

<span>Each lady has 2 feet and each cat has 4 feet </span>

<span><=> </span>

<span>x + y = 26 (1) => number of characters </span>
<span>2x + 4y = 84 (2) => number of feet </span>

<span><=> operation : (1) * 2 </span>

<span>2x + 2y = 52 (1') </span>
<span>2x + 4y = 88 (2') </span>

<span><=> operation : (2') - (1') </span>

<span>2y = 26 </span>

<span><=> </span>

<span>y = 20 and x = 32- 16 = 16</span>

<span>10 ladies and 16 cats</span>
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