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Lena [83]
2 years ago
12

Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer she would pay $2,350 down a

nd $200 each month. At another dealer, she would pay $2,750 down and $175 each month. After how many months would the total amount paid be the same for both dealers? What would that amount be?
After
_____months Kenya will have paid $_____
for the bike at either dealer.
Mathematics
1 answer:
vovangra [49]2 years ago
8 0

Answer:

After 16 months, Kenya will have paid $5,550

Step-by-step explanation:

This is a guess and check type of a problem.  You guess a number of months, plug it into x, and see if both equations come out with the same answer.

 If you plug 16 into the first dealer's equation, you get y= 200(16) + 2350.  Solving this equation will mean y equals 5550.

If you plug 16 into the second dealer's equation, you get y= 175(16) + 2750.

Solving this equation will mean y also equals 5550.

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Answer:

The number of each type in the pack is 5 of $0.45 comic books and 9 of $0.75 comic books

Step-by-step explanation:

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, the unknowns or unknown variables are:

x: number of $ 0.45 comic books

y: number of $ 0.75 comic books

Jacques wants to make up packs of $0.45 comic books mixed with $0.75 ones to sell at $9.00 per pack.  Then the equation that represents this situation is:

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On the other side, the number of $0.45 comic books is 4 more than the number of $0.75 comic books.  Then the equation that represents this situation is:

x+4=y

The system of equations to solve is:

\left \{ {{x*0.45+y*0.75=9} \atop {x+4=y}} \right.

One way to solve a system of equations is the substitution method, which consists of solving one of the unknowns in one of the equations and substituting its value in the next.

In this case we directly replace the expression of the variable and of the second equation in the first:

x*0.45 + (x+4)*0.75= 9

Solving:

x*0.45 + 0.75*x + 4*0.75= 9

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1.2*x= 9-3

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x=5

Replacing this value in the expression x+4=y you get:

5 +4=y

9=y

<u><em>The number of each type in the pack is 5 of $0.45 comic books and 9 of $0.75 comic books</em></u>

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