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# systems of equations

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67 water barrels need to be carried by trucks and cars. 2 trucks and 5 cars can carry them all. If 3 trucks and 4 cars are used, there will be 5 barrels left. Determine how many barrels each truck and car can carry.

Aug 6, 2022

#1
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If we use these numbers, and do the math, then Your problem makes absolutely no sense.

If it is so that 3T + 4C leaves room for 5 more barrels, it seems to make more sense, but even en then

we come up with fractions for C, so I advice You to repost the problem with adjusted numbers.

Original numbers:

Water barrels:just numbers, Trucks: T, Cars: C

67 = 2T + 5C

67 - 5 = 3T + 5C, or 67 = 3T + 5C +5

Setting the first line equal to the second:

2T + 5C = 3T + 5C + 5, we subtract 5C on both sides, eliminiating C, and get

2T = 3T + 5, or T = -5  :: This makes absolutely NO sense.

Put this into the topmost line:

67 = -10 + 5C, 77 = 5C, C = 77/5 :: Also makes NO sense.

67 = 2T + 5C

67 + 5 = 3T + 5C, or 67 = 3T + 5C -5

2T + 5C = 3T + 5C - 5

2T = 3T - 5, or T = 5

Put into topmost:

67 = 10 + 5C, 5C = 57, and so C = 11 2/5 :: Also makes no sense.

Aug 6, 2022
#2
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T==Trucks,    C==Cars

2T  +  5C ==67

3T  +  4C ==67 - 5, solve for C, T

C ==11 water barrels per car !!!!!

T ==6 water barrels per truck !!!!

Note: It does give integer solution, but the problem is that each car carries 11 barrels vs 6 barrels per truck!!, which defies common sense!!

Aug 6, 2022