Question #866bc

2 Answers
Nov 26, 2016

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#

Nov 26, 2016

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]