Question

Tina is saving to buy a notebook computer. She has two options. The first option is to put $200 away initially and save $10 every month. The second option is to put $100 away initially and save $30 every month. After how many months would Tina save the same amount using either option? How much would she save with either option?

Answer 1

Answer:

5 Months and Tina's saving after 5 months from either of the given options would be $250

Step-by-step explanation:

Option 1

Tina saves $200 away initially and save $10 every month

Let Tina save for X month, then her total saving after X month would be =  

$200 + $10X

Option 2

Tina saves $100 away initially and save $30 every month

Let Tina save for X month, then her total saving after X month would be =  

$100 + $30X

The savings from two options must be equal at the end of X months.  

$200 + $10X = $100 + $30X

$200 - $100 = $30X - $10X

$100 = $20X

X = $100/$20  

= 5

So Tina will save equal amount from both the options if she saves for 5 months.  

Her saving after 5 months through both the options  

Option 1 : $200 + $10X = $200 + $10 x 5 = $250

Option 2 : $100 + $30X = $100 + $30 x 5 = $250

Answer 2

The correct answers are:

It would take 5 months and she would save $250.

Explanation:

Let m be the number of months.

For the first way of saving, $200 up front and $10 each month, the expression would be

200+10m.

For the second way of saving, $100 up front and $30 each month, the expression would be

100+30m.

Setting them equal gives us the equation

200+10m = 100+30m

Subtract 10m from each side:

200+10m-10m = 100+30m-10m

200 = 100+20m

Subtract 100 from each side:

200-100 = 100+20m-100

100 = 20m

Divide both sides by 20:

100/20 = 20m/20

5 = m

It would take 5 months.

$200 up front and $10 each month for 5 months:

200+10m

200+10(5)

200+50

250

She would save $250.