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# how to solve proportions with variables

Question:another number. For example: 3/(x-4) = 7/(x+5) I learned this over two years ago, and I can't remember how to do it. Does anyone know how?

Answers:You need to get all of the x on one side. To do this, cross multiply, then isolate x from the numbers. 3(x+5) = 7(x-4) 3x + 15 = 7x - 28 -4x = -43 x = 10.75

Question:Okay, I'm in 6th grade, and for my math homework we have to solve proportions. For example: x/21 = 6/7. In this case, x would equal 18. I know how to use algebra to solve the proportion when the variable is in the numerator of the fraction, but I get confused when the variable is in the denominator. I can still get the answer by just finding out how both numerators or denominators relate to each other, but my math teacher wants us to solve them using algebra, and she wants to see all the steps. Can someone please explain to me how to solve the proportions if the letter variable is in the denominator? I'm still getting confused. I know that in the proportion x/21 = 6/7, I have to multiply each side of the proportion by 21/1. However, if it were 21/x = 7/6, would I multiply each side of the proportion by 1/21?

Answers:Use cross multiplication: Okay you say that you are confused if x is in the denominator, so I made this problem: 6/9=216/x First, multiply the denominator of the first fraction by the numerator of the second fraction and multiply the numerator of the first fraction by the denominator of the second fraction, like so: 9*216=6*x to get 1944=6x Now divide both sides by 6 to get x alone 1944/6=6x/6 to get 324=x

Question:x-4 / 5 = x+2 / 7 the 5 and the 7 are underneath please show me how you get the answers too if possible, ty so much!

Answers:You solve this like any other proportion: 1. Find the cross products. 2. Solve the equation by isolating the variable. x - 4 ... x + 2 ____ = _____ ...5 .... 7 7(x -4) = 5(x + 2) -----------------> Set up the cross factors 7x - 28 = 5x + 10 -----------------> Multiply to find cross products 2x -28 = +10 ------------------------> Solve to isolate "x" by first subtracting 5x from each side of = 2x = +38 ---------------------------> Next divide both sides by 2 x = 19

Question:I don't want the answer, i just want an example on how to do these problems. 5/3c = 2/3 24/5 = 9/y+2 5/m+1 = 4m/m my book doesn't show examples on how to figure these out! it's frustrating :( I'm clueless on what to do...

Answers:a) 5/3c= 2/3 To isolate 'c', divide both sides by '5/3'. Remember, dividing by a fraction is the same as multiplying by it's reciprocal. in otherwords, c= 2/3 divided by 5/3 Is the same as c= 2/3 times 3/5. 2x3=6. 3x5=15. Therefore c=6/15 The numerator and the denominator are both divisible by 3. Therefore c=2/5. b). Remember to first isolate the variable. Subtract 2 from both sides: 24/5 -2 = 9/y Rearrange this equation to isolate the variable. y(24/5 -2) = 9 Make it neater by changing (-2) into a fraction over 5: -10/5 y(24/5 -10/5) = 9 Simplify: y (14/5)= 9 To isolate y, divide both sides by 14/5. Change 9 into 9/1 in order to make the switching easier: y= 9/1 divided by 14/5 which becomes y= 9/1 times 5/14 y= 45/14 This fraction isn't reducable, so it stays 45/14. c) 5/m+ 1 = 4m/m Remember that when you divide 4m/m, because there are no exponents, the 'm's cancel: 5/m +1= 4 5/m= 3 3m= 5 m= 5/3 Remember, you can always double check your answer by plugging the final answer into the original equation and solving it.