Just for fun since I have nothing to do today, I want you to write a system of equations to solve this puzzle, and solve by using substitution.
If four times the larger number is added to two times the smaller number, the result is 14. When the larger number is reduced by two times the smaller number, the difference is 1. What are the numbers?
Good luck. (:
2007-12-04 08:34:27 · 12 answers · asked by rykster22 1 in Science & Mathematics ➔ Mathematics
1 and 3
2007-12-04 08:37:49 · answer #1 · answered by Elizabeth 7 · 0⤊ 0⤋
Let a be the larger number and b the smaller number. Then two equations arise:
(1) 4a + 2b = 14
(2) a - 2b = 1
From equation 2: a = 1+2b
Substituting the expression for a into the first equation leads to:
4(1+2b) + 2b = 14
4 + 10b = 14
Thus b = 1.
Since a = 1+2b it equals 1+2(1) = 3.
If this was just for fun though, why use substitution when elimination would have been so much cleaner?
2007-12-04 08:43:10 · answer #2 · answered by bloodninja 3 · 0⤊ 0⤋
1
2007-12-04 08:37:03 · answer #3 · answered by ThE BrAiN 2 · 0⤊ 1⤋
Let s= smaller number, and l= larger number
4l+2s=14
I'll get back to this later...
l-2s=1
1=1 +2s
Back.
4(1+2s) + 2s = 14
4 + 8s + 2s = 14
4+10s = 14
10s = 10
s = 1
Plug it into 2nd equation:
l-2(1)=1
l- 2 = 1
l = 3
To check:
4(3) + 2(1) = 14
12+ 2 = 14
14 = 14
Smaller Number: 1
Larger Number: 3
2007-12-04 08:40:40 · answer #4 · answered by mikezcim 5 · 0⤊ 0⤋
Call the larger number L and the smaller S.
4L + 2S = 14
L - 2S = 1
From the second one, L = 1 + 2S, sub into the first.
4(1+2S) + 2S = 14
4 + 8S + 2S = 14
10S + 4 = 14
10S = 10
S = 1
From L = 1 + 2S, L = 1 + 2(1) ----> L = 3
So, the two numbers are 1 and 3.
2007-12-04 08:39:51 · answer #5 · answered by Scott Evil 6 · 0⤊ 0⤋
Larger number= 3
Smaller number= 1
2007-12-04 08:41:35 · answer #6 · answered by doofyee 2 · 0⤊ 0⤋
Let L be the larger number and s be the smaller number.
4L + 2s = 14
L - 2s = 1
L = 1 + 2s
4(1+2s)+2s = 14
4 +10s = 14
10s=10
s=1
L - 2 = 1
L = 3
2007-12-04 08:37:55 · answer #7 · answered by lhvinny 7 · 0⤊ 0⤋
The numbers are 5 and 2.
:-)
2007-12-04 08:37:13 · answer #8 · answered by Anonymous · 0⤊ 1⤋
4L + 2S = 14
L - 2S = 1
L = 1 + 2S
Substituting for L:
4(1 + 2S) + 2S = 14
4 + 8S +2S = 14
4 + 10S = 14
10S = 10
S = 1
L = 1 + 2(1)
L = 3
Smaller number = 1
Larger number = 3
2007-12-04 08:40:27 · answer #9 · answered by Zandia 3 · 0⤊ 0⤋
write down the numbers on index taking part in cards so as which you will flow them around like a actual puzzle. bear in mind which you're probable going to need an excellent sort with a small sort and medium sized numbers to function jointly. solid success :)
2016-10-19 04:05:53 · answer #10 · answered by ? 4 · 0⤊ 0⤋