Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Brittany and Winston each opened a savings account on the same day. Brittany started by putting $209 in her account, and she will deposit an additional $176 each week. Winston made an initial deposit of $699, and he will add $127 more each week. Eventually, Brittany and Winston will each have the same amount saved. How many weeks will that take? What is that amount?

Respuesta :

Given that Brittany started by putting $209 in her account, she will deposit an additional $176 each week.

Winston made an initial deposit of $699, and he will add $127 more each week.

Let x be the number of weeks.

The equation for Brittany is

[tex]B=209+176x[/tex]

The equation for Winston is

[tex]W=699+127x[/tex]

Brittany and Winston will each have the same amount saved.

So we get B=W.

Substitute equations, we get

[tex]209+176x=699+127x[/tex]

Subtracting 209 from both sides, we get

[tex]209+176x-209=699+127x-209[/tex]

[tex]176x=127x+490[/tex]

Subtracting 127x from both sides, we get

[tex]176x-127x=127x+490-127x[/tex]

[tex]49x=490[/tex]

Dividing both sides by 49, we get

[tex]\frac{49x}{49}=\frac{490}{49}[/tex][tex]x=10[/tex]

The number of weeks =10 weeks.

[tex]\text{ Substitute x=10 in 209+176x, we get}[/tex][tex]209+176(10)=209+1760=1969[/tex]

The amount is $1969.

Hence after 10 weeks, Brittany and Winston each have $1969 in their account.

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