SOLUTION: Lopez spent 1/3 of his vacation money for travel and 2/5 of his vacation money for lodging. He spent $1100 for travel and lodging. What is the total amount of money he spent on his

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Question 1042246: Lopez spent 1/3 of his vacation money for travel and 2/5 of his vacation money for lodging. He spent $1100 for travel and lodging. What is the total amount of money he spent on his vacation?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = total amount spent on his vacation
+%281%2F3%29%2Ax+ for travel
+%282%2F5%29%2Ax+ for lodging
+%281%2F3%29%2Ax+%2B+%282%2F5%29%2Ax+=+1100+
Multiply both sides by +15+
+5x+%2B+3x+=+16500+
+8x+=+16500+
+x+=+2062.5+
He spent $2,062.50 on vacation

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Lopez spent 1/3 of his vacation money for travel and 2/5 of his vacation money for lodging. He spent $1100 for travel and lodging. What is the total amount of money he spent on his vacation?
 He spent matrix%281%2C5%2C+1%2F3+%2B+2%2F5%2C+or%2C+5%2F15+%2B+6%2F15%2C+or%2C+11%2F15%29%29 of vacation money on travel and lodging. This fraction represents $1,100. With A being the total amount spent, 

we get the following proportion: %2811%2F15%29%2F1+=+%22%241%2C100%22%2FA

11A%2F15+=+%22%241%2C100%22 ------- Cross-multiplying

11A = 15($1,100) ------- Cross-multiplying

A, or amount spent on vacation = matrix%281%2C1%2C+%2215%28%241%2C100%29%22%2F11%29 = highlight_green%28%22%241%2C500%22%29