Best friends, Olivia and Sylvia both get a weekly allowance, Olivia and Sylvia’s allowances are in the ratio 2:3 if Sylvia gets $21 one week how much did Olivia get use a tape diagram to help organize your thinking
To find out how much Olivia gets, we can set up a proportion based on the ratio of their allowances.
The ratio of Olivia's allowance to Sylvia's allowance is 2:3.
Let's set up the proportion:
2/3 = x/21
Cross-multiplying, we get:
3x = 2 * 21
3x = 42
Dividing both sides by 3, we find:
x = 42/3
x = 14
Therefore, Olivia got $14 for that week.
You can use a tape diagram to represent the proportion visually. Let's draw a rectangle and divide it into two parts based on the ratio of their allowances:
Olivia : Sylvia
__________ __________
| | | |
| | | |
|__________| |__________|
Since the ratio is 2:3, we can divide the rectangle into 2 parts for Olivia and 3 parts for Sylvia. Since Sylvia gets $21, we can label her part as $21. Then, we can label Olivia's part as x, as we are trying to find out her amount.
Olivia : Sylvia
__________ __________
| x | | $21 |
|__________| |__________|
Using the proportion, we found out that x is equal to $14, so we can label Olivia's part as $14:
Olivia : Sylvia
__________ __________
| $14 | | $21 |
|__________| |__________|
Hence, Olivia got $14 for that week.
Let's represent Olivia's allowance as x and Sylvia's allowance as y.
According to the given ratio, we have the equation:
x/y = 2/3
We know that Sylvia gets $21, so we can substitute y with 21 in the equation:
x/21 = 2/3
To find the value of x, we can cross-multiply:
3x = 2 * 21
3x = 42
Dividing both sides by 3:
x = 42/3
x = 14
Therefore, Olivia got $14.
To find out how much Olivia got, we can use the ratio of their allowances.
Given that the ratio of their allowances is 2:3 and Sylvia gets $21, we can set up the equation:
2/3 = Olivia's Allowance/Sylvia's Allowance
Now we can solve for Olivia's allowance:
Olivia's Allowance = (2/3) * Sylvia's Allowance
Substituting Sylvia's Allowance as $21, we have:
Olivia's Allowance = (2/3) * $21
To solve this equation mentally, we can first simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 1:
Olivia's Allowance = (2/3) * $21 = (2 * $21) / 3
Now we can perform the multiplication:
Olivia's Allowance = $42 / 3 = $14
So Olivia got $14 as her allowance.
Regarding the tape diagram, we can draw a rectangle and divide it into two parts, representing the ratios of 2:3. One part can be labeled as Olivia's Allowance, and the other part as Sylvia's Allowance. Since Sylvia gets $21, we can label that amount on her part of the rectangle. Then we can determine the corresponding amount for Olivia based on the ratio.