Alex has $20, and Ellen has $12. Alex is saving $3 per day, and Ellen is saving $5 per day. After how many days will Alex and Ellen have the same amount of money?
A) 3 days
B) 4 days***
C) 5 days
D) 10 days
Yes, B.
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It's 100% B
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Would this be the same as saying 4×12 and 4×20 for the above question
Yes, you can also solve the problem by calculating how many days it would take for both Alex and Ellen to save the same amount of money by multiplying their daily savings by the number of days.
Alex's savings: $3/day x 4 days = $12
Ellen's savings: $5/day x 4 days = $20
So after 4 days, both Alex and Ellen will have the same amount of money, which confirms the answer B.
Can this be made into a equation if we have to explain it that way?
Yes, we can express the problem as an equation to solve for the number of days it will take for Alex and Ellen to have the same amount of money.
Let's define:
x = number of days
Alex's total savings = 20 + 3x
Ellen's total savings = 12 + 5x
To find the point where they have the same amount of money, we set their total savings equal to each other and solve for x:
20 + 3x = 12 + 5x
We can simplify:
3x - 5x = 12 - 20
-2x = -8
Divide by -2:
x = 4
So it will take 4 days for Alex and Ellen to have the same amount of money.