Question
Janna has some 50 cents coins. If she spends $2.50 each day, she will have 3 coins left. If she spends $4 each day, she'll have 7 coins left. What is the minimum amount of money that she has?
Steps to solve question 2 using the model drawing method.
1. $2.50 = Five 50-cent coins $1.50 = Three 50-cent coins
$4 = Eight 50-cent coins $3.50 = Seven 50-cent coins
2. Since the amount of the money must be the same for both cases, we will draw two equal length bars.
3. First Bar : 5 : 3 : :
Second Bar : 8 : 7 : :
4. Next, we will add 8 into the empty space in the second bar
First Bar : 5 : 3 : :
Second Bar : 8 : 7 : 8 :
5 7 + 8 = 15
since 15 can be divided by 5, we will not add more 8s into the empty space in the second bar.
6. Hence,
First Bar : 5 : 3 : 5 : 5 : 5 :
Second Bar : 8 : 7 : 8 :
7. So, the minimum amount of money she has = (8 + 7 + 8)coins x 50 cents
= $11.50
Alternatively, the minimum amount of money she has
= (5 + 3 + 5 + 5 + 5) coins x 50 cents = $11.50