How can I show a bar model for this problem?
Naomi Macy and Sebastian have 234 stamps in all. Naomi gives 16 stamps to Macy and 24 stamps to Sebastian. Naomi then has 3 times as many stamps as Macy, and Macy has twice as many stamps as Sebastian. how many stamps does Naomi have at first?
Well, let's see if we can create a "humorous" bar model for this problem.
Naomi Macy and Sebastian went to a stamp convention. They had a total of 234 stamps with them. Naomi being the generous one, gave 16 stamps to Macy and 24 stamps to Sebastian.
Now, imagine we have three colorful candy bars representing the number of stamps Naomi, Macy, and Sebastian have. Each candy bar represents a different number of stamps.
Before the stamp-giving extravaganza, let's give each person a candy bar to hold, just to keep things fair. So, Naomi starts off with a full candy bar, Macy has half of that, and Sebastian gets a measly quarter of the candy bar.
Then, Naomi goes wild and gives away some stamps. She gives Macy 16, which means Macy's candy bar grows a bit. But it's not just any growth - it doubles in size! Macy's candy bar becomes the same length as Naomi's, but still half as long as this description.
Next, Naomi decides to spoil Sebastian a little and gives him 24 stamps. Sebastian's candy bar grows too, but not as much as Macy's. It becomes half the length of Macy's candy bar. (Poor Sebastian could use a bit more candy to match Macy's, but we'll have to stick with the given numbers.)
Now, let's take a look at how the candy bars are looking. We know that Naomi has 3 times the number of stamps as Macy. In candy bar terms, Naomi's candy bar is three times longer than Macy's candy bar.
Since we're dealing with candy bars, not actual numbers, let's assume that Naomi's candy bar is 3 units long. Then, Macy's candy bar is 1 unit long (since it's half the length of Naomi's), and Sebastian's candy bar is 0.5 units long (since it's half the length of Macy's).
According to the problem, the total length of all the candy bars combined is 234 stamps. So, let's calculate the actual lengths of the candy bars:
Naomi's candy bar (3 units) + Macy's candy bar (1 unit) + Sebastian's candy bar (0.5 units) = 4.5 units
And we know that the total length is actually equal to 234 stamps. So:
4.5 units = 234 stamps
To find out how many stamps are in each unit, we can divide 234 by 4.5:
234 / 4.5 ≈ 52
So, each unit is approximately equal to 52 stamps.
Now, since Naomi's candy bar is 3 units long, we can multiply the length by the number of stamps per unit:
3 units * 52 stamps per unit = 156 stamps
Therefore, Naomi had 156 stamps at first before giving any away.
To show a bar model for this problem, you will need to represent the quantities mentioned in the problem with bars.
Start by drawing a bar to represent the total number of stamps they have at the beginning. Let's call this bar 'Total' and label it as 234.
Next, you need to represent the quantity of stamps that Naomi gives to Macy and Sebastian. Draw a bar next to the 'Total' bar and label it 'Given to Macy' with a value of 16. Draw another bar and label it 'Given to Sebastian' with a value of 24.
Now, you can represent the remaining stamps for each person. Draw a bar next to the 'Given to Macy' bar and label it 'Naomi's Remaining' with a value of (Total - Given to Macy). Similarly, draw a bar next to the 'Given to Sebastian' bar and label it 'Macy's Remaining' with a value of (Total - Given to Sebastian).
Finally, you can represent the relationship between the three people's stamps. According to the problem, Naomi has three times as many stamps as Macy, and Macy has twice as many stamps as Sebastian. To represent this, draw a bar next to 'Naomi's Remaining' bar and label it 'Macy's stamps' with a value of (Naomi's Remaining / 3). Draw another bar next to the 'Macy's Remaining' bar and label it 'Sebastian's stamps' with a value of (Macy's Remaining / 2).
To find out how many stamps Naomi has at the beginning, you need to add up the values of 'Naomi's Remaining', 'Macy's stamps', and 'Given to Macy' from the bar model.
Let's calculate it:
Naomi's Remaining = Total - Given to Macy = 234 - 16 = 218
Macy's stamps = Naomi's Remaining / 3 = 218 / 3 ≈ 72.67 (rounded to the nearest whole number)
Since the values need to be whole numbers, let's adjust them while maintaining the relationship. We can add 1 to 'Macy's stamps' and subtract 3 from 'Naomi's Remaining'.
Naomi's Remaining = 218 - 3 = 215
Macy's stamps = 72 + 1 = 73
Now, let's calculate Naomi's stamps at first:
Naomi's stamps at first = Naomi's Remaining + Macy's stamps + Given to Macy = 215 + 73 + 16 = 304
Therefore, Naomi had 304 stamps at the beginning.