Question

One pound of swordfish costs as much as 1.5 pounds of salmon. Mrs. O pays $39 for 2 pounds of salmon and 3 pounds of swordfish. Find the ratio of the amount of money Mrs. O pays for the swordfish to the amount of money she pays for the swordfish.

I know the answer is 9:4, but how would you do this without algebra?

Answer 1

The ratio of the amount for swordfish to the amount of salmon is 6:4

Explanation:

Given as :

The price for 1 pound of swordfish = The price of 1.5 pound of salmon

So, On this relation

The price for ( 1 × 2 ) pound of swordfish = The price of ( 1.5× 2 ) pound of salmon

i.e The price for 2 pound of swordfish = The price of 3 pound of salmon

Now According to question

Mrs. O pay the total money for 2 pounds of swordfish and 3 pound of salmon = $ 39

Let the money she pay for swordfish = 2 sw

And The money she pay for salmon = 3 sa

∵, The total money she pay for both = $ 39

I.e 2 sw + 3 sa = 39

As 2 sw = 3 sa

So, 3 sa + 3 sa = 39

Or, 6 sa = 39

or, sa =
`(39)/(6)` =
`(13)/(2)`

∴ sw =
`(13)/(2)` ×
`(3)/(2)`

or, sw =
`(39)/(4)`

Now, the ratio of the amount for swordfish to the amount of salmon =
`((39)/(4))/((13)/(2))`

I.e The ratio =
`(6)/(4)`

Hence The ratio of the amount for swordfish to the amount of salmon is 6:4

Answer