Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs $200 more than the size below it. Alan spends a total of $3,400. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?
A. 850
B. 1,100
C. 1,700
D. 2,550
E. 3,400
The OA is C.
I'm confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
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Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch...
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BTGmoderatorLU
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Hello LUANDATO.
Let's take a look at your question.
TV1= x $, TV2= x+200 $, TV3= x+400 $ and TV4= x+600 $.
We now that $$3400=x+\left(x+200\right)+\left(x+400\right)+\left(x+600\right)=4x+1200 $$ $$3400=4x+1200\ \Leftrightarrow\ 4x=2200\ \Leftrightarrow\ x=550.$$ Therefore, the 28 inch Tv cost 750$ and the 30 inch Tv cost 950$.
Hence, if Alan had bought only the 28 inch and 30 inch TVs, he had spent only 750$+950$=1700$.
This is why the correct answer is the option C.
I'm available if you'd like a follow-up.
Regards.
Let's take a look at your question.
TV1= x $, TV2= x+200 $, TV3= x+400 $ and TV4= x+600 $.
We now that $$3400=x+\left(x+200\right)+\left(x+400\right)+\left(x+600\right)=4x+1200 $$ $$3400=4x+1200\ \Leftrightarrow\ 4x=2200\ \Leftrightarrow\ x=550.$$ Therefore, the 28 inch Tv cost 750$ and the 30 inch Tv cost 950$.
Hence, if Alan had bought only the 28 inch and 30 inch TVs, he had spent only 750$+950$=1700$.
This is why the correct answer is the option C.
I'm available if you'd like a follow-up.
Regards.
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We can let x = the cost of the 26-inch TV; thus, x + 200, x + 400 and x + 600 are the costs of the 28-inch, 30-inch and 32-in TVs, respectively. Since the total cost of the 28-inch and 30-inch TVs is 2x + 600, which is the same as the total cost of the 26-inch and 32-inch TVs, we see that the total cost of the 28-inch and 30-inch TVs must be half of the total cost of $3,400, or $1,700.BTGmoderatorLU wrote:Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs $200 more than the size below it. Alan spends a total of $3,400. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?
A. 850
B. 1,100
C. 1,700
D. 2,550
E. 3,400
The OA is C.
I'm confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
Answer: C
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