Let's break down the problem step-by-step.
### Step 1: Identify the Problem
Tanya wants to save for a vacation. She needs to have at least [tex]$75 for each of the 12 days of her trip. First, we need to find out how much money she needs in total.
### Step 2: Calculate the Total Amount Needed
To find the total amount of money Tanya needs, multiply the daily amount by the number of days:
\[ \text{Total Needed} = 75 \, \text{dollars/day} \times 12 \, \text{days} \]
### Step 3: Calculate the Total Money Saved
Tanya saves $[/tex]85 each month for 10 months. To find the total money she saves, multiply the monthly saving amount by the number of months:
[tex]\[ \text{Total Saved} = 85 \, \text{dollars/month} \times 10 \, \text{months} \][/tex]
### Step 4: Compare the Total Needed and Total Saved
We need to determine if the total amount she has saved is enough to cover her trip expenses. This is checked by verifying if the total saved is greater than or equal to the total needed.
### Solution
Based on our calculations, the total amount Tanya needs is [tex]\(75 \times 12\)[/tex] dollars, which is [tex]$900. The total amount she saves is \(85 \times 10\) dollars, which is $[/tex]850.
Total Needed: [tex]\(900\)[/tex] dollars \
Total Saved: [tex]\(850\)[/tex] dollars
### Conclusion
Since [tex]$850 (total saved) is less than $[/tex]900 (total needed), Tanya will not have saved enough money for her trip.
### Different Approach Explanation
Jorge suggested comparing [tex]\(85 \times 10\)[/tex] and [tex]\(75 \times 12\)[/tex]. We agree with this approach because both multiplications will give the total amounts directly to be compared.
- [tex]\(85 \times 10 = 850\)[/tex]
- [tex]\(75 \times 12 = 900\)[/tex]
By comparing these two results, we can clearly see that [tex]\(850 < 900\)[/tex], confirming again that Tanya does not have enough savings for her trip.
