Best friends Olivia and Sylvia both get a weekly allowance. Olivia’s 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 solve this problem, we can first set up a ratio between Olivia's and Sylvia's allowances. Since Sylvia's allowance is $21, we can represent her allowance as 3 parts. This means that Olivia's allowance is 2 parts.
To find Olivia's allowance, we need to determine the value of one part. Since Sylvia's allowance is 3 parts and equals $21, we can divide $21 by 3 to find the value of one part.
$21 ÷ 3 = $<<21/3=7>>7
So, one part represents $7.
Now, we can find Olivia's allowance by multiplying her share of parts (2 parts) by the value of one part.
2 parts × $7 = $<<2*7=14>>14
Therefore, Olivia received $14.
To find out how much Olivia got, we need to set up a proportion using the ratio of their allowances.
The ratio of Olivia’s allowance to Sylvia’s allowance is 2:3.
Let's assume Olivia's allowance as x dollars.
According to the given information, Sylvia gets $21.
So, we can set up the following proportion:
2/3 = x/21
To solve for x, we can cross-multiply.
2 * 21 = 3x
42 = 3x
Next, we divide both sides by 3 to solve for x:
42/3 = x
14 = x
Therefore, Olivia got $14 as her allowance.
To find out how much Olivia got, we need to determine the multiplier in the ratio.
The ratio of Olivia's allowance to Sylvia's allowance is 2:3. This can be represented by drawing a tape diagram with two parts for Olivia and three parts for Sylvia.
Since Sylvia's allowance is given as $21, we can use this information to find the value of each part in the tape diagram.
We know that three parts equal $21, so to find the value of one part, we divide $21 by 3:
$21 ÷ 3 = $7
Now, we can use the multiplier to find out how much Olivia got. The multiplier is the number we need to multiply the value of one part by to find the value of Olivia's allowance.
Since Olivia's and Sylvia's allowances have a ratio of 2:3, the multiplier is 2.
To find how much Olivia got, we multiply $7 (the value of one part) by 2 (the multiplier):
$7 x 2 = $14
Therefore, Olivia got $14.