QuestionMaria has \$50 and saves money weekly to buy a \$200 TV. After 3 weeks, she has \$122. How many more weeks to save?

Studdy Solution

STEP 1

Assumptions1. Maria's initial amount is $50. . The cost of the television is$ 200.
3. Maria's savings increase at a constant rate each week.
4. The amount saved after the first week is $74.<br />5. The amount saved after the second week is$ 98.
6. The amount saved after the third week is $122.

STEP 2

First, we need to determine the weekly saving rate. We can do this by subtracting the initial amount from the amount saved after the first week.
$Weekly\, saving\, rate = Amount\, after\, first\, week - Initial\, amount$

STEP 3

Now, plug in the given values for the initial amount and the amount after the first week to calculate the weekly saving rate.
$Weekly\, saving\, rate = \$74 - \$50$

STEP 4

Calculate the weekly saving rate.
$Weekly\, saving\, rate = \$74 - \$50 = \$24$

STEP 5

Now that we have the weekly saving rate, we can find the total number of weeks Maria needs to save to buy the television. This can be done by subtracting the initial amount from the cost of the television and dividing the result by the weekly saving rate.
$Number\, of\, weeks = (Cost\, of\, television - Initial\, amount) / Weekly\, saving\, rate$

STEP 6

Plug in the values for the cost of the television, the initial amount, and the weekly saving rate to calculate the number of weeks.
$Number\, of\, weeks = (\$200 - \$50) / \$24$

STEP 7

Calculate the number of weeks.
$Number\, of\, weeks = (\$200 - \$50) / \$24 =6.25$ Since the number of weeks cannot be a fraction, Maria will have to save for7 weeks to have enough money to buy the television.

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