Question

Question #866bc

Answer 1

Each dog has $40.00 spent on it.

Explanation:

Objective: find the cost for `ul("each")` dog.

Let the cost for 1 dog be `d`
Let the cost for 1 cat be `c`
Let total cost be `t`

Count of cats is 164
Count of dogs is 24
Total budget is $4240 `= t`
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`color(blue)("Building the equations")`

Breaking down part of the question into its component parts:

...for each dog cost twice as much as those supplies for cats.

`=> d=2c`................Equation(1)

Feeds 164 cats and 24 dogs. Her budget is $4240.

`=>t=164c+24d`.........Equation(2)

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`color(blue)("Determine the cost of the dogs")`

Consider equation(1): `=> c=d/2" " ..............Equation(1_a)`

Using `Equation(1_a)` substitute for cats in Equation(2) giving:

`t=164(d/2)+24d`

But `t=$4240`

`$4240=164(d/2)+24d`

`$4240" "=" "82d+24d" " =" " 106d`

Divide both sides by 106

`d=$4240/106 = $40.00`

Answer 2

Jane can spend `$40` on each dog for food and medication.

Explanation:

Let `$x` be the cost of food and medication of single cat.

Then, `$(2*x)` is the cost of food and medication of single dog.

By condition `24*2x+164x=4240 or 48x+164x=4240 or 212x=4240 or x= 4240/212=$20 ; 2x=$40`

Hence Jane can spend `$40` on each dog for food and medication. [Ans]