Question

When the price of a dozen eggs is raised by $2.4, 15 fewer eggs can be bought with $60.
(a) Find the original price of an egg.
(b) How many eggs can be bought after raising the price?

Answer 1

@satellite73 would you kindly help me?

Answer 2

we can do this

Answer 3

lets call the price per egg, which we don't know, as \(x\)
then if the price goes up by $2.4 a dozen, then it goes up by \(2.4\div 12=0.2\) per egg

Answer 4

yup

Answer 5

i am sure there is an easier way to do this but i will continue

Answer 6

if we call the number of eggs bought for $60 \(y\) then before the price increase we have
\[xy=60\] and after the price increase we have
\[(x+.2)(y-15)=60\]

Answer 7

y is ?

Answer 8

something tells me there is an easier way, but i can't see it at the moment

Answer 9

\(y\) is the number of eggs you can buy for \(\$60\) before the price increase

Answer 10

ok

Answer 11

that is why \(xy=60\)

Answer 12

or we can say \(x=\frac{60}{y}\) that is the original price per egg

Answer 13

that turns the equation
\[(x+.2)(y-15)=60\] into
\[(\frac{60}{y}+0.2)(y-15)=60\] and you can solve this for \(y\)

Answer 14

so the equations are:
xy=60
(x+0.2)(y-15)=60 ?

Answer 15

or for that matter you can solve
\[(x+0.2)(\frac{60}{x}-15)\]

Answer 16

wait a second, let me calculate

Answer 17

i have an answer, i am not sure i like it, but i have one

Answer 18

lol my calculation is wrong, i got 40 something

Answer 19

i got \(x=4\) and \(y=75\)

Answer 20

meaning originally you paid $4 per egg, which seems rather steep
then again so does a $2.40 price per dozen increase
are you sure it was not $.24 ?

Answer 21

the answer of part a is $0.8

Answer 22

it is $2.40 increase, or \(\$.24\) per dozen

Answer 23

can you show me your working steps? maybe i got my steps wrong

Answer 24

you mean in solving the equation, or how i got the equation?

Answer 25

solving the equation

Answer 26

ooohhhh!!!! i made a mistake
you are right, it is \(.8\)

Answer 27

the answer is 0.8, but i can't get it

Answer 28

solve \[(x+0.2)(\frac{60}{x}-15)=60\]

Answer 29

i got 43.33333.....

Answer 30

umm

Answer 31

okay we can work out the steps

Answer 32

is it?