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.
Let's represent the ratio of Olivia's and Sylvia's allowances as 2x:3x.
We know that Sylvia gets $21 one week, which represents 3x. So, we can set up the equation 3x = 21.
To find x, we divide both sides of the equation by 3. 3x/3 = 21/3, which simplifies to x = 7.
Now, we can find Olivia's allowance by multiplying her ratio (2x) by x. Olivia gets 2 * 7 = $<<2*7=14>>14. Answer: \boxed{14}.
To find out how much Olivia got as an allowance, we can set up a proportion based on the given ratio.
Let's assume Olivia's allowance as "x" dollars.
According to the ratio 2:3, we can set up the following proportion:
2/3 = x/21
To solve for x, we can cross-multiply:
2 * 21 = 3 * x
42 = 3 * x
Divide both sides by 3 to isolate x:
x = 42/3
x = 14
Therefore, Olivia received $14 as her allowance for that week.
To represent this using a tape diagram, we can draw two separate sections for Olivia and Sylvia's allowances. Since the ratio is given as 2:3, we can divide the tape into two sections with different lengths but in the ratio of 2:3. Olivia's section will be shorter than Sylvia's.
Olivia's tape diagram:
|----|----|
Sylvia's tape diagram:
|----|----|----|
Given that Sylvia received $21 for that week, we can cut Sylvia's tape into three equal parts and determine the value of each part:
|----|----|----| => $21
Now we can compare the lengths of the sections to find Olivia's allowance.
|----|----| => $14
Hence, Olivia received $14 as her allowance.
To solve this problem using a tape diagram, we can represent Olivia's and Sylvia's allowances as two parts of a whole.
Let's start by representing Sylvia's allowance of $21. We can draw a rectangle and divide it into three equal parts. Each part represents $7, since $21 divided by 3 is $7.
*<-----$7----->*<-----$7----->*<-----$7----->*
Now, we need to find Olivia's allowance. The ratio of Olivia's to Sylvia's allowance is 2:3. Since Sylvia's allowance is represented by three parts, we need to use two parts to represent Olivia's allowance.
$7 + $7 = $14
So, Olivia's allowance is $14.