Question 951875: Hi!! I am learning the substitution method with systems of equations and the elimination method!! how do I start solving this problem? 'Four times the larger of two numbers is equal to seven times the smaller. The sum of the numbers is 22. Find the numbers.'
thanks!
Found 2 solutions by ptaylor, MathTherapy:
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Here's a good way to start:
Let x= larger number
And let y= smaller. umber
Now we are told that:
4x=7y--------eq1
We are also told that:
x+y=22-----eq2
Substitution method looks easier.
From eq1 x=(7/4)y. Substitute this into eq2
(7 /4)y +y=22
(7/4)y+(4/4)y=22
(11/4)y=22 multiply each side by 4
11y=88
y=8
From eq2, x+8=22
x=14
Hope this helps ---ptaylor
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website!
Hi!! I am learning the substitution method with systems of equations and the elimination method!! how do I start solving this problem? 'Four times the larger of two numbers is equal to seven times the smaller. The sum of the numbers is 22. Find the numbers.'
thanks!
Method 1: SUBSTITUTION
Let larger number be L, and smaller, S. Then, we get:
4L = 7S ------- eq (i)
L + S = 22______L = 22 - S ------ eq (ii)
4(22 - S) = 7S ------- Substituting 22 - S for L in eq (i)
Continue to solve for S, or smaller number. Then substitute the value for S into any of the
2 original equation to determine the value of L, the larger number.
Method 2: ELIMINATION
Let larger number be L, and smaller, S. Then, we get:
4L = 7S______4L - 7S = 0 ------- eq (i)
L + S = 22 ------ eq (ii)
- 4L - 4S = - 88 ------ Multiplying eq (ii) by - 4 to ELIMINATE L ------- eq (iii)
- 11S = - 88 ------ Adding eqs (iii) & (i)
Continue to solve for S, or smaller number. Then substitute the value for S into any of the
2 original equation to determine the value of L, the larger number.
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