Question

I need help TODAY

Robert needs to cut four shelves from a board that is 2.5 meters long. The second shelf is 18 centimeters longer than twice the length of the first shelf. The third shelf is 12 centimeters shorter than the first shelf. The remaining shelf is 4 centimeters longer than the first shelf. If Robert must use the entire 2.5 meter board for the shelves, what is the length of the second shelf, in centimeters?

Answer 1

ok... hmmm we know the length of the board is just 2.5meters

let's say
a = first shelf
b = second shelf
c = third shelf
d = fourth shelf

so, we know their sum must be 2.5, or a + b + c + d = 2.5

now, what is twice the first one? or "a"? 2*a or 2a, now, what's 18 longer than 2a? 2a + 18
so b = 2a + 18

now, what is 12 shorter than "a"? well a - 12
so c = a - 12

and the "remaining", namely "d", is 4 longer than "a"
so d = a + 4

so
`\bf a+b+c+d=2.5 \begin{cases} b=2a+18\\ c=a-12\\ d=a+4 \end{cases} \\\\\\ a+(2a+18)+(a-12)+(a+4)=2.5`

solve for "a"

how long is the second shelf? well b = 2a + 18