Word problems

[Yukki_cross]

So i can get the equation into the cordnaits but I can't get the words into the problem: Four times the larger of two numbers is equal to seven times the smaller. The sum of the numbers is 22. Find the numbers

 

[soroban]

Hello, Yukki_cross!

So i can get the equation into the coordinates, but I can't get the words into the problem:
Four times the larger of two numbers is equal to seven times the smaller. The sum of the numbers is 22.
Find the numbers.

Name things!

Let \(\displaystyle x\) = the larger number.
Let \(\displaystyle y\) = the smaller numbers.


Now what does it say?

\(\displaystyle \underbrace{\text{Four}}_4 \underbrace{\text{times}}_{\times} \underbrace{\text{the larger}}_x \underbrace{\text{is equal to }}_{=} \underbrace{\text{seven}}_7 \underbrace{\text{times}}_{\times} \underbrace{\text{the smaller}}_{y}\)

. . We have: .\(\displaystyle 4x \:=\:7y\) .[1]


\(\displaystyle \underbrace{\text{Sum of the numbers}}_{x+y} \underbrace{\text{is}}_= \underbrace{\text{12}}_{12}\)

. . We have: .\(\displaystyle x + y \:=\:12\) .[2]


Solve the system of equations . . .

 

[Mrspi]

Hello, Yukki_cross!


Name things!

Let \(\displaystyle x\) = the larger number.
Let \(\displaystyle y\) = the smaller numbers.


Now what does it say?

\(\displaystyle \underbrace{\text{Four}}_4 \underbrace{\text{times}}_{\times} \underbrace{\text{the larger}}_x \underbrace{\text{is equal to }}_{=} \underbrace{\text{seven}}_7 \underbrace{\text{times}}_{\times} \underbrace{\text{the smaller}}_{y}\)

. . We have: .\(\displaystyle 4x \:=\:7y\) .[1]


\(\displaystyle \underbrace{\text{Sum of the numbers}}_{x+y} \underbrace{\text{is}}_= \underbrace{\text{12}}_{12}\)

. . We have: .\(\displaystyle x + y \:=\:12\) .[2]


Solve the system of equations . . .

Soroban, I have the UTMOST respect for your knowledge and the quality of your answers....but....


PLEASE do not use "x" to indicate multiplication!

You, of all people, should realize what kinds of problems that can cause.

If YOU do it (use x for multiplication) you're giving that terribly sloppy notation legitimacy. I don't think you would want to do that.

 

[soroban]

Hello, Mrspi!

Of course, you're right!

I did use both \(\displaystyle x\) and \(\displaystyle \times\),
. . hoping that difference would be significant.

I like using the \(\displaystyle \times\) sign under the word "times",
. . but I should have used other variables.
\(\displaystyle a\) and \(\displaystyle b\), or \(\displaystyle L\) and \(\displaystyle S\) would be safer.