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Problem 52

Three numbers sum up to 147 . The smallest number is half the middle number, which is half the largest
number. What are the three numbers?

the system has no solution.

## Discussion

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## Video Transcript

All right, So 52 is the word problem that has to do with a system of three equations and three unknowns. The sign of the unknowns are three members. We know the three numbers add up to 1 40 center. We know that the small number is half the middle number and the little numbers large. So let's start out by defining our very bulls. So it's may excuse me with a small, um, Why? Unequal middle and C b the large. Okay, so we know that X plus y plus z equals 1 47 We know that x news. Half of why, and we know why. Chapel. All right, So, um, to do a little bit of substitution here. Um, yes. Uh, if we substitute, um, 1/2 z do a substitution here, we substitute one, Have z for why we get that X is not only 1/2 of why, but it's also 14 See? All right, so now what we have is by substituting these values this for Why Jesus, Laura? Meaning? Substitute this for the why and so this for X. And we'll have one equation that only has two seats for the very day. So one for see is equal to I'm sorry. One Ford C plus one Pepsi. Plus, is it? So asked me. 1 47 All right, Um, let me see 1/2. One board is re force. The force was four horse this seven ports. So we get seven wars, See equals 1 47 by both sides. But for over seven, get Z is equal to one of the seven times for 84. So she is 84. That means why is half of that according to and X is half of that. It could be 21 just to check. Seven, 12 13 14 1 47 Adds up. All right, so good.