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!