Question

15 points
pls help fast with all questions
thank you

Answer 1

11a

`3x\\ 4x\\ 10+2x\\ 12+2x`

11b

`8\\ 6\\ 7\\ 6`

12

Anna is 18. Rita is 13.

13

Mark is 12.

Explanation:

Recall that the perimeter of a shape is the sum (or total) of all the edges that make up that shape. So, for the first shape, there are three Xs. We write this as
`\bold{3x}` so this is the perimeter.

In the second, there are four Xs, so this is
`\bold{4x}`.

In the third, there are two Xs and two 5s, so this is
`2x+(2*5)=\bold{10+2x}`.

In the fourth, there are two Xs and three 4s, so this is
`2x+(3*4)=\bold{12+2x}`.

If each is equal to 24, we can simply set them as equal to 24 and solve.

`3x = 24\\\bold{x=8}`

----

`4x=24\\ \bold{x=6}`

----

`10+2x=24\\2x = 14\\\bold{x=7}`

----

`12+2x=24\\2x=12\\\bold{x=6}`

If Anna is 5 years older than Rita, then
`a=r+5`. If their sum is 31, then
`a+r=31`. We can perform some substitution:

`(r+5)+r=31\\5+2r=31\\2r=26\\r=13`

Therefore, Rita is 13. Keep going:

`a=r+5\\a=13+5\\a=18`

Anna is 18.

If Dad is three times as old as Mark, then
`d=3m`. If the sum of their ages is 48, then
`d+m=48`. We can perform some algebra:

`d+m=48\\m=48-d\\d=3(48-d)\\d=144-3d\\4d=144\\d=36`

Dad is 36. Keep going:

`d=3m\\36=3m\\m=12`

Mark is 12.

Now that you've seen these, you do the bonus ;)