SOLUTION: Let x represent the smaller number and y the larger number. The sum of the two numbers is 200. If the larger number is 8 less than triple the smaller number, what are the two numbe

Question 1203234: Let x represent the smaller number and y the larger number. The sum of the two numbers is 200. If the larger number is 8 less than triple the smaller number, what are the two numbers?
The sum of two numbers is 200. But I’m confused as to write if the larger number is 8 less than triple the
X=200-y -> x=200-178.05 smaller #
X=-y+200
Replace y with 178.05
X=-178.05+200
X=21.95

Found 5 solutions by MathLover1, math_tutor2020, ikleyn, greenestamps, josgarithmetic:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

given:
=>smaller number
=>larger number

.....eq.1
....eq.2

from eq.1 and eq.2 we have

go to eq.1 and substitute

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = smaller number
y = larger number

x+y = 200 because the two numbers sum to 200

"The larger number is 8 less than triple the smaller" means
larger = 3*smaller - 8
y = 3x - 8

We can plug this into the first equation to solve for x
x+y = 200
x+y = 200
x+3x-8 = 200
4x-8 = 200
4x = 200+8
4x = 208
x = 208/4
x = 52

Then,
y = 3x-8
y = 3*52-8
y = 156-8
y = 148

Answer: The two numbers are 52 and 148.

Check: 52+148 = 200

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Let x represent the smaller number and y the larger number.
The sum of the two numbers is 200. If the larger number is 8 less
than triple the smaller number, what are the two numbers?
The sum of two numbers is 200. But I’m confused as to write if the larger number is 8 less than triple the
X=200-y -> x=200-178.05 smaller #
X=-y+200
Replace y with 178.05
X=-178.05+200
X=21.95
~~~~~~~~~~~~~~~~~~

x = smaller unknown number; y = greater unknown number. First equation x + y = 200 (1) does not require explanations Second equation y = 3x - 8 (2) "the larger number is 8 less than triple the smaller number" To solve, we substitute y = 3x-8 from equation (2) into equation (1). In other words, we REPLACE y in equation (1) by this expression y = 3x-8. We get then x + (3x-8) = 200. Now we have one equation for one single unknown x. To solve it, simplify it step by step x + 3x - 8 = 200 4x = 200+8 4x = 208 x = 208/4 = 52. Thus x is just found. To find y, use equation (2) y = 3x-8 = 3*52-8 = 148. ANSWER. x= 52, y= 148, CHECK. x + y = 52 + 148 = 200.

Solved, checked and explained.

Questions?

-----------------

If there are no questions, then the only thing that remained incomplete,
is to post me your "THANKS" for my teaching.

On the way, you learned how the substitution method works for this problem.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

You are told to let x be the smaller number and y be the larger number. Then...

(1) The sum of the two numbers is 200
x+y=200
You wrote x=-y+200
That is equivalent to the basic equation, but harder to work with. Leave the equation exactly as the words in the problem give it to you.

(2) The larger number is 8 less than triple the smaller number

It appears that you wrote an equation using the number 178.05. Where did that number come from? Maybe your work on paper is messy like mine usually is, and that number sneaked in from a different problem....

Translating that given information into algebraic language is a crucial skill. Take it a little bit at a time:
the smaller number: x
triple the smaller number: 3x
8 less than triple the smaller number: 3x-8

The larger number is 8 less than triple the smaller number: y=3x-8

Note many beginning students go in the wrong direction here by trying to translate word for word into algebraic language, ending up with "y=8-3x". But you have to listen to the whole phrase; 8 less than triple the smaller number means the "8" is subtracted from "triple the smaller number".

So from (1) and (2) we have the system of equations
x+y=200
y=3x-8

With the two equations in those forms, they are perfectly set up for solving by substitution; substitute "3x-8" for "y" in the first equation and go from there, as tutor @ikleyn does.

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
---------------------------------------------------------------------
If the larger number is 8 less than triple the smaller number,
---------------------------------------------------------------------

y, the larger number
x, the smaller number

, literally!
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