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 create a tape diagram, we start by dividing the total amount of money Sylvia received into 3 equal parts because her allowance is in the ratio 2:3.
Each part represents $21/3 = $7.
Since Olivia's allowance is in a 2:3 ratio, Olivia will receive 2 parts of $7 each.
Therefore, Olivia received $7 x 2 = $<<7*2=14>>14. Answer: \boxed{14}.
To find out how much Olivia got, we can use a tape diagram to represent the ratio of their allowances.
Step 1: Draw a rectangle to represent the total allowance.
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Step 2: Divide the rectangle into 5 equal parts to represent the total ratio of 2:3.
-- -- -- -- --
Step 3: Label the two parts representing Olivia's allowance and the three parts representing Sylvia's allowance.
OO OO -- -- --
Step 4: Since Sylvia got $21, we know that the three parts representing her allowance equal $21.
OO OO $21 $21 $21
Step 5: Divide $21 equally among the three parts.
OO OO $7 $7 $7
Step 6: Olivia's share is represented by the two parts remaining.
OO OO $7 $7 $7
Step 7: Olivia's total allowance is $14.
Therefore, Olivia got $14.
To solve this problem, we can use a tape diagram to represent the given information visually.
A tape diagram is a type of visual model that uses rectangles to represent parts of a whole. In this case, we can use the rectangles to represent the amounts of money Olivia and Sylvia receive as their weekly allowances. Since Olivia's and Sylvia's allowances are in the ratio 2:3, we can represent Olivia's allowance with a rectangle divided into 2 equal parts and Sylvia's allowance with a rectangle divided into 3 equal parts. Let's draw the tape diagram.
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Olivia Sylvia
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Now that we have the tape diagram set up, we know that Sylvia's allowance is $21, which corresponds to 3 equal parts of her rectangle. So, we can divide her rectangle into 3 equal parts and label one of the parts as $21.
```
Olivia Sylvia
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| | | $21 |
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To figure out Olivia's allowance, we can use the ratio of 2:3. Since each part represents the same amount, we can multiply $21 by 2/3 to find out how much money Olivia gets.
$21 * 2/3 = $14
Therefore, Olivia gets $14 as her weekly allowance.