QuestionHow many cows did Bill get if Dan has 42 cows and they split them in a 5:7 ratio?

Studdy Solution

STEP 1

Assumptions1. The herd of cows is split between Bill and Dan in the ratio57. . Dan's share of the cows is42.

STEP 2

First, we need to find out how many parts the total number of cows is divided into. We can do this by adding the two numbers in the ratio.
$Total\, parts = Bill's\, ratio + Dan's\, ratio$

STEP 3

Now, plug in the given values for Bill's ratio and Dan's ratio to calculate the total parts.
$Total\, parts =5 +7$

STEP 4

Calculate the total parts.
$Total\, parts = +7 =12$

STEP 5

Now that we have the total parts, we can find out how many cows each part represents. We do this by dividing Dan's share of the cows by Dan's ratio.
$Cows\, per\, part = Dan's\, share / Dan's\, ratio$

STEP 6

Plug in the values for Dan's share and Dan's ratio to calculate the cows per part.
$Cows\, per\, part =42 /$

STEP 7

Calculate the cows per part.
$Cows\, per\, part =42 /7 =6$

STEP 8

Now that we have the number of cows each part represents, we can find out how many cows Bill got. We do this by multiplying the number of cows per part by Bill's ratio.
$Bill's\, share = Cows\, per\, part \\times Bill's\, ratio$

STEP 9

Plug in the values for cows per part and Bill's ratio to calculate Bill's share.
$Bill's\, share =6 \\times5$

STEP 10

Calculate Bill's share.
$Bill's\, share =6 \\times5 =30$ Bill got30 cows.

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