Question

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?

Answer 1

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

$B=209+176x$

The equation for Winston is

$W=699+127x$

Brittany and Winston will each have the same amount saved.

So we get B=W.

Substitute equations, we get

$209+176x=699+127x$

Subtracting 209 from both sides, we get

$209+176x-209=699+127x-209$

$176x=127x+490$

Subtracting 127x from both sides, we get

$176x-127x=127x+490-127x$

$49x=490$

Dividing both sides by 49, we get

$\frac{49x}{49}=\frac{490}{49}$$x=10$

The number of weeks =10 weeks.

$\text{ Substitute x=10 in 209+176x, we get}$$209+176(10)=209+1760=1969$

The amount is $1969.

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