Question

Solve the following problems using the 5D process.

(Describe/Draw, Define, Do, Decide, and and Declare)​

Answer 1

First problem: let
`b` and
`h` be the base and height of the rectangle, respectively. We know that
`b=11+h` (the base if 11 longer than the height), and that
`2(b+h)=58` (the perimeter is 58 centimeters).

So, we have the system

`\begin{cases}b=11+h\\2(b+h)=58\end{cases}\iff\begin{cases}b=11+h\\b+h=29\end{cases}`

Use the first equation to substitute into the second:

`b+h=11+h+h=2h+11=29 \iff 2h=18 \iff h=9`

And since the base is 11 centimeters longer, we have

`b=11+h=11+9=20`

Second problem: Let
`m,n,o` be the number of cards owned by Mark, Norm and Oscar, respectively. We know that:

`m+n+o=810` (they have 810 cards in total)

`n=m+30` (Norm has 30 more than Mark)

`o=2m` (Oscar has twice as much as Mark)

The second and third equation express
`n` and
`o` in terms of
`m`, and substituting those expressions in the first equation we have

`m+n+o=m+(m+30)+2m=810 \iff 4m+30=810 \iff 4m=780 \iff m=195`

And then we can use again the second and third equations:

`n=m+30=195+30=225`

`o=2m=2\cdot 195=390`