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Solve each problem by using a system of three equations inthree unknowns.

The sum of the digits of a three-digit number is 11 dollars . If the digits are reversed, the new number is 46 more than five times the old number. If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number?

137

Algebra

Algebra 2

Chapter 4

Systems of Linear Equations

Section 3

Systems of Linear Equations in Three Variables

Polynomials

Systems of Equations and Inequalities

Introduction to Algebra

Graph Linear Functions

Write Linear Equations

Linear Equations and Functions

Matrices and Determinants

University of California, Berkeley

University of Washington

Oregon State University

University of Michigan - Ann Arbor

Lectures

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03:45

01:05

Write a system of two equa…

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Find a three-digit number …

all right. So he were given kind of a tricky word problem for system of equations. Um, we're told it's a three digit number. Uh, the some of the digits X y z equals 11. And then we're told Ruthy Digit Plus two is it equals the memorable kind of confusing way that if the digits are reversed, the new number is 46 more than five times the older number. Okay, so I'm just gonna write that over here. It's reversed. New number, old plus 46. Um, we could write an equation for this, um, and then solve using substitution and elimination. But instead, let's try to just use these two equations that we have to actually solve. We can rewrite. The second equation is X plus two y minus Z zero. This. Now, look, use elimination. Uh, yeah, these two equations, we're going to act plus three y close 11. There's gonna give us ax equals 11 minus three wide. About two by two announcing logically about what possible values for why could be We know that acts has to be a positive integer X has to be a positive the doctor and we know that. Why also has to be a positive industry between zero and nine. Um, any value of why that's greater than three. It's gonna give us a negative number here, so it can't be greater than three. And, uh, this has to be. It has to yield a positive interest here as well. Right? So it can't be too, because I would give you five halves. Um, can't be zero, because I would give you 11 halfs. So the only possible values of why are one and three We only have two possible values. Weaken. Guess in check. Um, and Saul for why? So it's try using. Why was three first? Um, if, like was three x is getting me cool. Alright. When Why goes three x is gonna equal 11 minus nine. That's too bad about two equals one and then z is gonna equal. We have appeared. If axes one plus six, that's seven. Mine is equal. Zero. Susie's getting cool. Seven. So now we have a number which is warm 37. Now, if to see if we reverse the digits. So if we have 700 and 31 does that equal five times 1 37 plus 46. Please put your calculators. You do five times 1 37 close 46. And that equals 731. So this answer checks out. If you tried play begin, like was one, you'd have gotten a three digit number. Um, that does not. But where this equation does not hold now we have our number 137.

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