Diego has $11 and begins saving $5 each week toward buying a new phone. At the same time that Diego begins saving, Lin has $60 and begins spending $2 per week on supplies for her art class. Is there a week when they have the same amount of money? How much do they have at the same time?
11, 16, 21, 26, 31, 36, 41, 46, 51
60, 58, 56, 54, 52, 50, 48, 46, 44
Takes 8 weeks and they meet up at 46$
7 weeks and $46 on desmos
7 weeks and $46 on desmos
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To determine if there is a week when Diego and Lin have the same amount of money, we need to analyze their savings over time. Let's start by looking at Diego's savings.
Diego saves $5 per week, so we can represent his savings as an arithmetic sequence with a common difference of 5. His savings after each week can be calculated using the formula:
Diego's savings = $11 + ($5 × number of weeks)
Now, let's examine Lin's spending.
Lin spends $2 per week, so we can represent her spending as an arithmetic sequence with a common difference of -2 (since she is spending). Her remaining balance after each week can be calculated using the formula:
Lin's remaining balance = $60 - ($2 × number of weeks)
To find the week when Diego and Lin have the same amount of money, we need to set Diego's savings equal to Lin's remaining balance:
$11 + ($5 × number of weeks) = $60 - ($2 × number of weeks)
Let's solve this equation to find the number of weeks it takes for Diego and Lin to have the same amount of money.
$11 + ($5 × number of weeks) = $60 - ($2 × number of weeks)
Now, we can simplify the equation:
$5 × number of weeks + $2 × number of weeks = $60 - $11
Combining like terms:
$7 × number of weeks = $49
Dividing both sides of the equation by 7:
number of weeks = $49 ÷ $7
number of weeks = 7
Therefore, Diego and Lin will have the same amount of money after 7 weeks. To find out how much money they will have at that time, we can substitute the value of the number of weeks into either Diego's savings or Lin's remaining balance equation. Let's choose Diego's savings equation:
Diego's savings = $11 + ($5 × number of weeks)
Diego's savings = $11 + ($5 × 7)
Diego's savings = $11 + $35
Diego's savings = $46
Therefore, after 7 weeks, both Diego and Lin will have $46.