Answer:
11a
[tex]3x\\ 4x\\ 10+2x\\ 12+2x[/tex]
11b
[tex]8\\ 6\\ 7\\ 6[/tex]
12
Anna is 18. Rita is 13.
13
Mark is 12.
Step-by-step 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 [tex]\bold{3x}[/tex] so this is the perimeter.
In the second, there are four Xs, so this is [tex]\bold{4x}[/tex].
In the third, there are two Xs and two 5s, so this is [tex]2x+(2*5)=\bold{10+2x}[/tex].
In the fourth, there are two Xs and three 4s, so this is [tex]2x+(3*4)=\bold{12+2x}[/tex].
If each is equal to 24, we can simply set them as equal to 24 and solve.
[tex]3x = 24\\\bold{x=8}[/tex]
----
[tex]4x=24\\ \bold{x=6}[/tex]
----
[tex]10+2x=24\\2x = 14\\\bold{x=7}[/tex]
----
[tex]12+2x=24\\2x=12\\\bold{x=6}[/tex]
If Anna is 5 years older than Rita, then [tex]a=r+5[/tex]. If their sum is 31, then [tex]a+r=31[/tex]. We can perform some substitution:
[tex](r+5)+r=31\\5+2r=31\\2r=26\\r=13[/tex]
Therefore, Rita is 13. Keep going:
[tex]a=r+5\\a=13+5\\a=18[/tex]
Anna is 18.
If Dad is three times as old as Mark, then [tex]d=3m[/tex]. If the sum of their ages is 48, then [tex]d+m=48[/tex]. We can perform some algebra:
[tex]d+m=48\\m=48-d\\d=3(48-d)\\d=144-3d\\4d=144\\d=36[/tex]
Dad is 36. Keep going:
[tex]d=3m\\36=3m\\m=12[/tex]
Mark is 12.
Now that you've seen these, you do the bonus ;)
