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.(1 point)
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Let's assume that Olivia gets $x as her allowance.
Since Sylvia's allowance is in the ratio 2:3 with Olivia's, we can set up the following equation:
2/3 = x/21
By cross multiplying, we have:
3x = 2 * 21
3x = 42
x = 42/3
x = 14
Therefore, Olivia got $14 as her allowance.
To find out how much Olivia gets, we can use the given ratio of their allowances, which is 2:3. Let's represent Olivia's allowance with 2x and Sylvia's allowance with 3x, where x is a variable representing the amount.
Since Sylvia gets $21, we can set up the equation:
3x = $21
Now we need to solve for x. Dividing both sides of the equation by 3 gives us:
x = $21/3
x = $7
Now that we know the value of x, we can find Olivia's allowance by substituting it into the expression 2x:
Olivia's allowance = 2x
Olivia's allowance = 2 * $7
Olivia's allowance = $14
Therefore, Olivia gets $14 as her weekly allowance.
To solve this problem, we can use a tape diagram to visualize the given information.
First, we need to understand the ratio between Olivia's and Sylvia's allowances, which is 2:3. This means that for every 2 parts Olivia gets, Sylvia gets 3 parts.
Since we know Sylvia's allowance is $21, we can find the value of 1 part by dividing $21 by 3, as Sylvia gets 3 parts.
$21 / 3 = $7
So, 1 part of the allowance is equal to $7.
Now, to find Olivia's allowance, we need to multiply 2 parts (Olivia's share) by the value of 1 part ($7).
2 * $7 = $14
Therefore, Olivia gets $14 as her allowance.