# Singapore math 5A, textbook p. 25 problem 10

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The answer is \$35 and I can get it by using algebra. How do I solve this without algebra?

"John and Paul spent \$45 altogether. John and Henry spent \$65 altogether. If Henry spent 3 times as much as Paul, how much did John spend? "

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I'll take a stab at this. I'm not so great at the bar diagrams online. :tongue_smilie:

Set up the problem like this:

<----\$45------>

[--John--][Paul]

[--John--][Paul]<-\$65-\$45->

<---------\$65----------- --->

[--John--][Paul][Paul][Paul]

[--John--]<---Henry------->

The difference between John/Paul and John/Henry is 2 units, which is equivalent to \$65-\$45 (\$20).

2 Units = \$20 Therefore 1 Unit (Paul) = \$10

If Paul (\$10) and John spent \$45 together, then \$45-\$10= \$35 spent by John

Henry spent 3 x \$10 (\$30). With John they spent \$65. So \$65-\$30 = \$35

Edited by plain jane
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what do you mean without algebra?

Will this be algebra?

j+p= 45

j+h=65

h=3p

j+p=45

j+3p=65

j=45-p

45-p+3p=65

j=45-p

2p=20

p=10

j=45-10

j=35

WOULD THIS BE ALGEBRA?

Edited by trying my best
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By "without algebra" I mean without setting up a system of equations using x and y BUT by using bar diagrams.

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I'll take a stab at this. I'm not so great at the bar diagrams online. :tongue_smilie:

Set up the problem like this:

<----\$45------>

[--John--][Paul]

[--John--][Paul]<-\$65-\$45->

<---------\$65----------- --->

[--John--][Paul][Paul][Paul]

[--John--]<---Henry------->

The difference between John/Paul and John/Henry is 2 units, which is equivalent to \$65-\$45 (\$20).

2 Units = \$20 Therefore 1 Unit (Paul) = \$10

If Paul (\$10) and John spent \$45 together, then \$45-\$10= \$35 spent by John

Henry spent 3 x \$10 (\$30). With John they spent \$65. So \$65-\$30 = \$35

Thanks! That's it!

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By "without algebra" I mean without setting up a system of equations using x and y BUT by using bar diagrams.

We never learned Bar Diagrams in school :confused:

in Russia they only taught us by algebra...

Something to learn for me :tongue_smilie:here.

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Do the bar things confuse you too? Gosh I don't know what it is but the bar diagrams do NOT speak to me.

I've been using SM since K and it's only been this year that the bar diagrams are starting to speak to me in any sort of language that makes sense. :tongue_smilie: I still can't wrap my head around a lot of them but I must say that when they click, it's a darn good feeling.

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I've been using SM since K and it's only been this year that the bar diagrams are starting to speak to me in any sort of language that makes sense. :tongue_smilie: I still can't wrap my head around a lot of them but I must say that when they click, it's a darn good feeling.

:iagree:

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Well, this is the first problem that I just could not do with the bar diagrams. Part of it was the pressure I felt from my son, saying, "See, even you can't do it. It's too hard for me". I guess I'll just have to start doing the word problems ahead of time.

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