Comments on: How do I translate this word problem to a workable equation? http://op-snj.org/translate/how-do-i-translate-this-word-problem-to-a-workable-equation Mon, 15 Feb 2010 22:52:59 -0600 http://wordpress.org/?v=2.8.2 hourly 1 By: Kat K http://op-snj.org/translate/how-do-i-translate-this-word-problem-to-a-workable-equation/comment-page-1#comment-4 Kat K Sat, 01 Aug 2009 09:34:59 +0000 http://op-snj.org/translate/how-do-i-translate-this-word-problem-to-a-workable-equation#comment-4 x - y = 16 and 3(x) = 7(y) <br><b>References : </b><br> x – y = 16 and 3(x) = 7(y)

References :

]]> By: Baganagalagachoogaboogaloogayay! http://op-snj.org/translate/how-do-i-translate-this-word-problem-to-a-workable-equation/comment-page-1#comment-3 Baganagalagachoogaboogaloogayay! Sat, 01 Aug 2009 08:58:59 +0000 http://op-snj.org/translate/how-do-i-translate-this-word-problem-to-a-workable-equation#comment-3 Let's first figure out what we don't know, and make those variables. We need to find 2 numbers that follow those two rules. Let's call those 2 numbers x and y. So the difference between the two numbers is 16. x - y = 16 Three times the larger number (x) is 7 times the smaller (y). So, 3 times the larger number is 3 * x = 3x 7 times the smaller = 7 * y = 7y 3x = 7y One way to solve a linear equation is called "substitution", when you find x = something not related to x, and then plug that into the equation. So since 3x = 7y, x = 7y/3 Plug that into x - y = 16 7y/3 - y = 16 Since y = 3y/3 (the threes cancel) 7y/3 - 3y/3 = 16 See the common denominators? Let's simplify. 4y/3 = 16 Let's divide both sides by 4 y/3 = 4 Multiply both sides of the equation by 3 y = 12 Now plug again into the equation for y and solve for x x - y = 16 x - 12 = 16 x = 28 The two numbers are 12 and 28. Hope this helped!<br><b>References : </b><br> Let’s first figure out what we don’t know, and make those variables.
We need to find 2 numbers that follow those two rules.
Let’s call those 2 numbers x and y.

So the difference between the two numbers is 16.
x – y = 16

Three times the larger number (x) is 7 times the smaller (y).
So, 3 times the larger number is 3 * x = 3x
7 times the smaller = 7 * y = 7y
3x = 7y

One way to solve a linear equation is called "substitution", when you find x = something not related to x, and then plug that into the equation.

So since 3x = 7y,
x = 7y/3

Plug that into x – y = 16

7y/3 – y = 16

Since y = 3y/3 (the threes cancel)

7y/3 – 3y/3 = 16

See the common denominators? Let’s simplify.

4y/3 = 16

Let’s divide both sides by 4

y/3 = 4

Multiply both sides of the equation by 3

y = 12

Now plug again into the equation for y and solve for x

x – y = 16
x – 12 = 16
x = 28

The two numbers are 12 and 28.

Hope this helped!
References :

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