Grade 9 math/ linear equations/word problem

Question

the sun takes 25.38 earth days to rotate once about the axis. This time is 3.92 earth days less than half the time that mercury takes to rotate about it's axis. how many earth days does mercury take to rotate about its axis once. Please explain all the steps and how to get the answer.

Answer 1

Hi Tanya:

We need an equation, relating the sun's rotation tom Mercury's.

Let S = time it takes the sun to rotate once on its axis.

Let M = time it takes mercury to rotate once on its axis.

Then, the question tells us that: S = M / 2 - 3.92 . . . . . . . . . . (eqn 1)

Now, rearrange the equation to get M by itself.

Add 3,02 to both sides of eqn 1: S + 3.92 = M / 2

Multiply through by 2: 2(S + 3.92) = M

This gives an equation for M.

Plug in 25.38 for S (given): M = 2(25.38 + 3.92)

= 2(29.3)

= 58.6 days