Best friends Olivia and Sylvia both get weekly allowances. Olivia's and Sylvia's allowances are in the ratio 2 : 3. If Sylvia gets $21 one weeks, how much did Olivia get? Use tape diagram to help organize you thinking.
To set up a tape diagram for this problem, we can represent Olivia's and Sylvia's allowances as two separate bars.
Let's use a pink bar to represent Olivia's allowance and a green bar to represent Sylvia's allowance.
Since the ratio of their allowances is 2:3, we can divide the pink bar into 2 equal parts and the green bar into 3 equal parts.
Now, we know that Sylvia got $21. We can divide the green bar into three equal parts and mark off $21 on one of those parts.
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Olivia Sylvia
Since the green bar represents Sylvia's allowance, we can see that $21 is one part out of three. Therefore, one part represents $21.
Now, we can determine how much each part is worth. We divide Sylvia's allowance by 3 to get the value of each part:
$21 ÷ 3 = $7
We found that each part represents $7.
Now, since the pink bar represents Olivia's allowance and there are 2 parts in the pink bar, we multiply the value of each part by 2 to get Olivia's allowance.
$7 × 2 = $14
Therefore, Olivia received $14 as her allowance.
To find out how much Olivia gets, we need to use the given information that the ratio of Olivia's allowance to Sylvia's allowance is 2:3.
Let's represent Olivia's allowance with 2 units and Sylvia's allowance with 3 units.
Since Sylvia gets $21, we can divide this amount into 3 equal parts. Each part represents one unit of Sylvia's allowance.
So, each unit represents $21/3 = $7.
Now, to find Olivia's allowance, we need to determine how many units Olivia gets based on the given ratio.
Since the ratio of Olivia's allowance to Sylvia's allowance is 2:3, Olivia would receive 2 units.
To find Olivia's allowance in dollars, we multiply the number of units (2) by the value per unit ($7):
Olivia's allowance = 2 units × $7/unit = $14.
Therefore, Olivia gets $14.
To find out how much Olivia got, we can use a tape diagram to represent the ratio of their allowances.
First, let's define the ratio: Olivia's allowance : Sylvia's allowance = 2 : 3.
We know that Sylvia's allowance is $21, and the ratio tells us that Sylvia's allowance is three parts. So, each part is $21 divided by 3, which equals $7.
Now, we need to find Olivia's allowance. Since Olivia's allowance is two parts, we take $7 multiplied by 2. Therefore, Olivia's allowance is $14.
So, Olivia got $14.