Question

A digital camera memory card is 1/4 full. The card is 2/3 full when 375 more pictures have been taken.

A) How many pictures can the memory card hold??

B) How many pictures were originally on the memory card??

Answer 1

To get the answer first we have to find full numbers.
We can use proportion
2/3 ----------------------- 375
1 -------------------------- x
Crossmultiply now
2/3*x=375 /:2/3
x=
`375: (2)/(3)`
x=
`375* (3)/(2)=562` - its the answer A)
Now we have to find how much were originally on the card.
To get the answer we can just multiply 562 times 1/4.
562*1/4=140 - its the asnwer B)

Answer 2

Let

x--------> total of images that the memory card can contain

we know that

`(2)/(3) x=(1)/(4) x+375`

Multiply by
`12` both sides

`8x=3x+375*12\\ 8x-3x=4,500\\ 5x=4,500\\ x=900 pictures`

originally on the memory card

`(1)/(4) x\\ =(1)/(4) *900\\ =225 pictures`

therefore

the answer part a) is

`900 pictures`

the answer part b) is

`225 pictures`