“Charlie would like to pack one less outfit than Jane for their trip. Loretta would like to bring five outfits less than twice what Jane packs. Due to space in the suitcase, they are limited to a total of 24 outfits. How many outfits can they each pack?”
first, we represent the unknowns using variables.
let x = outfits that Jane packed
let x-1 = outfits that Charlie packed
let 2x-5 = outfits that Loretta packed
since "limited to a total of 24 outfits", it means that the maximum number of outfits is 24:
x + (x-1) + (2x-5) <= 24
note: <= means less than or equal to
solving,
4x - 6 <= 24
4x <= 30
x <= 7.5
but since outfits cannot be a decimal/fraction, we take
x = 7 (the max number of outfit that Jane can pack)
and thus,
x-1 = 6 (max number of outfit that Charlie can pack)
2x-5 = 9 (max number of outfit that Loretta can pack)
hope this helps~ :)
If Jane packs x "outfits", the total number packed is
x + (x-1) + (2x -5) =or< 25
4x -6 =or< 25
4x <or= 31, and x must be an integer
x <or= 7 is Jane's number
6 is Charlie's maximum
9 is Loretta's maximum
They will not use up the available space if they stick to the rules relative to each other. There is room for two more outfits, unless I made a mistake along the way. See what you get
To answer this question, we need to set up a system of equations based on the information provided.
Let's call the number of outfits Jane packs "J".
According to the first statement, Charlie would like to pack one less outfit than Jane, so the number of outfits Charlie packs can be represented as "J - 1".
According to the second statement, Loretta would like to bring five outfits less than twice what Jane packs. Therefore, Loretta's number of outfits can be represented as "2J - 5".
The total number of outfits that they can collectively bring is limited to 24. So, we can add the numbers of outfits each person packs together and set it equal to 24:
J + (J - 1) + (2J - 5) = 24
Now, we can solve this equation to find the number of outfits each person can pack.
Combining like terms, we have:
4J - 6 = 24
Adding 6 to both sides of the equation:
4J = 30
Dividing both sides by 4:
J = 7.5
Since it doesn't make sense for Jane to pack a fraction of an outfit, we need to find a whole number. This means Jane can pack either 7 or 8 outfits.
If Jane packs 7 outfits:
- Charlie would pack one less, which is 6 outfits (J - 1 = 7 - 1 = 6).
- Loretta would pack five outfits less than twice what Jane packs, which is 9 outfits (2J - 5 = 2 * 7 - 5 = 14 - 5 = 9).
If Jane packs 8 outfits:
- Charlie would pack one less, which is 7 outfits (J - 1 = 8 - 1 = 7).
- Loretta would pack five outfits less than twice what Jane packs, which is 11 outfits (2J - 5 = 2 * 8 - 5 = 16 - 5 = 11).
So, it is possible for Jane to pack either 7 or 8 outfits, and then Charlie would pack either 6 or 7 outfits, and Loretta would pack either 9 or 11 outfits.