SOLUTION: Find two consecutive integers such that the sum of 3 times the first integer and 7 times second integer is 97.

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Question 111316: Find two consecutive integers such that the sum of 3 times the first integer and 7 times second integer is 97.
Found 2 solutions by HyperBrain, MathLover1:
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=the first integer
____x+1=the second integer

3x%2B7%2A%28x%2B1%29=97
3x%2B7x%2B7=97
10x%2B7=97
10x%2B7-7=97-7
10x%2B0=90
10x=90
x=9
x%2B1=10
tHUS, THE NUMBERS ARE 9, and 10!
Power up,
HyperBrain!

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Let first consecutive integer be x, and let second consecutive integer be y+=+x%2B1
Then:
3x+%2B+7y+=+97

3x+%2B+7%28x%2B1%29+=+97
3x+%2B+7x+%2B+7+=+97….move 7 to the right

+10x++=+97+-+7
+10x++=+90………..divide both sides by 10
+10x%2F10++=+90%2F10………..
+x++=+9………..first consecutive integer
Now find second consecutive integer
y+=+x%2B1+=+9+%2B+1
y+=+10……………….. second consecutive integer

Check:
3x+%2B+7y+=+97
3%2A9+%2B+7%2810%29+=+97
27+%2B+70+=+97