Hey :)

I'm sitting my maths non-calculator GCSE tomorrow and am currently revising. I'm doing a practise paper and am currently stuck on this question:

Express A in terms of w.

3w + 20 A
-------- = --------
200 A + 12

-- What does the question mean?

-- Can you explain to me step by step how to solve this problem? I'm really bad with understanding maths lingo btw :)


Thank you!

Arg, that problem is supposed to be

3w + 20
-------
200

is equal to

A
----
A + 12

write it like this, it is easier to read in this format.

(3w+20)/200 = A/(A+12)

cross-multiply to get
(3w+20)(A+12) = 200A
3Aw + 36w + 20A + 240 = 200A
3Aw - 180A = -240 - 36w
switch all the signs
180A - 3Aw = 240 + 36w
factor out an A
A(180 - 3w) = 240 + 36w
divide by 180 - 3w

A = (240+36w)/(180-3w)
A = (80+12w)/(60-w)

Hi! I'm here to help you with your math question. Don't worry, I'll break it down step by step for you.

In this question, you're asked to express A (a variable) in terms of w (another variable).

Let's go through the steps to solve this problem:

Step 1: Cross-multiply the fractions. This means multiplying the numerator of the left fraction (3w + 20) with the denominator of the right fraction (A + 12), and vice versa.

(3w + 20)(A + 12) = 200A

Step 2: Apply the distributive property by multiplying each term in the parentheses with each term outside the parentheses.

3w(A + 12) + 20(A + 12) = 200A

Step 3: Simplify the expression by multiplying each term.

3wA + 36w + 20A + 240 = 200A

Step 4: Combine like terms by grouping the terms with the same variables together.

(3wA + 20A) + (36w + 240) = 200A

Step 5: Simplify the expression further.

3wA + 20A + 36w + 240 = 200A

Step 6: Subtract 200A from both sides of the equation to isolate the variable A on one side of the equation.

3wA + 20A + 36w + 240 - 200A = 0

3wA - 180A + 36w + 240 = 0

Step 7: Combine like terms.

(3wA - 180A) + 36w + 240 = 0

Step 8: Simplify the expression further.

(wA - 60A) + 36w + 240 = 0

Step 9: Factor out the common factors from the terms containing A.

A(w - 60) + 36w + 240 = 0

Step 10: Now, we want to isolate A, so let's move the other terms to the right side.

A(w - 60) = -36w - 240

Step 11: Divide both sides of the equation by (w - 60) to solve for A.

A = (-36w - 240) / (w - 60)

That's it! You have now expressed A in terms of w. Let me know if you have any further questions or need more clarification. Good luck with your exam!