Ed saved $50 one week. For the next six weeks, he saved $25 more than the week before. how much did he save in all? one student sloved this problem using the expression $50 + 6($25)=200 What error was made? What is the right anwser?
The same amount was not added every week. Instead complete this table:
Week...Amt.Saved....Total
1.........50.........50
2.........75.........125
3.........100........225
4.........125........350
etc.
725
1st week=$50
2nd week=$75
3rd week=$100
4th week=$125
5th week=$150
6th week=$175
7th week=$200
TOTAL=$875
Y=20x+50
The error in the expression $50 + 6($25) = 200 is that it does not account for the increasing amount Ed saved each week. This expression only calculates the value of the initial $50 and does not consider the additional $25 saved each week.
To calculate the total amount Ed saved, we need to consider the increasing amount he saved each week. The correct approach is to add the initial $50 to the increasing amount saved each week.
To find the increasing amount, we can set up a pattern based on the given information. Ed saved $25 more than the week before for six weeks. So, we can represent this pattern as follows:
Week 1: $25 + $50
Week 2: $25 + ($25 + $50)
Week 3: $25 + ($25 + $25 + $50)
Week 4: $25 + ($25 + $25 + $25 + $50)
Week 5: $25 + ($25 + $25 + $25 + $25 + $50)
Week 6: $25 + ($25 + $25 + $25 + $25 + $25 + $50)
By simplifying these expressions, we can calculate the total amount saved by adding the corresponding terms:
$50 + $75 + $100 + $125 + $150 + $175 + $200 = $875
Therefore, Ed saved a total of $875 in all, not $200 as shown in the given expression.