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Hi,Could you please clarify the meaning of this sentence:"There are 3 fewer than 4 times as many dogs as cats"Many thanks,Nessie.

Mister Micawber · Accepted Answer

There are 10 cats.
There are 37 dogs. (10 x 4) -3

Nessie000 · Answer

Hi MM,
Thank you very much for the answer. But do you mean '10 cats' here is the hypothesis? (because that information was not given).
Many thanks once again,
Nessie.

BarbaraPA · Answer

Hi nessie,

The number of cats is C. We don't know what it is.

The number of dogs is 4C-3.

I speculate that Mr. M used "10 cats" as an example so it didn't look so much like an algebra equation (which is what it is).

CalifJim · Answer

nessie000Could you please clarify the meaning of this sentence:

"There are 3 fewer than 4 times as many dogs as cats"

Start with something simpler.

There are [five times as many] children as parents.
= There are more children than parents. In fact, if you multiply the number of parents by 5, you will know the number of children.

There are [twice as many (two times as many)] shirts as sweaters.
= There are more shirts than sweaters. In fact, if you multiply the number of sweaters by 2, you will know the number of shirts.

There are [two fewer than [three times as many]] chairs as tables.
= There are more chairs than tables. In fact, if you multiply the number of tables by 3 -- and then subtract 2 -- you will know the number of chairs.

There are 7 more than 4 times as many pens as pencils.
= There are more pens than pencils. In fact, if you multiply the number of tables by 4 -- and then add 7 -- you will know the number of pens.
____

In each case the number of the last things mentioned is unknown, but if it were known, you could proceed from that to figure out the number of the other things, because the sentence tells you the mathematical relationship between the two kinds of things, without telling you the actual number of either one or the other.

CJ

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