66 cupcakes are left in total
Step-by-step explanation:
The given is:
We need to find how many cupcakes are left in total
Assume that she mad x chocolate cupcakes and y vanilla cupcakes
∵ Emily made x chocolate cupcakes
∵ She made y vanilla cupcakes
∵ She made 130 chocolate cupcakes and vanilla cupcakes
- Add x and y, then equate the sum by 130
∴ x + y = 130 ⇒ (1)
∵ [tex]\frac{2}{3}[/tex] of the chocolate cupcakes were eaten
∴ The chocolate cupcakes were eaten = [tex]\frac{2}{3}[/tex] × x =
- Find the chocolate cupcakes were left by subtracting [tex]\frac{2}{3}[/tex] x from x
∴ The chocolate cupcakes were left = x - [tex]\frac{2}{3}[/tex] x = [tex]\frac{1}{3}[/tex] x
∵ [tex]\frac{2}{5}[/tex] of the vanilla cupcakes were eaten
∴ The vanilla cupcakes were eaten = [tex]\frac{2}{5}[/tex] × y =
- Find the vanilla cupcakes were left by subtracting [tex]\frac{2}{5}[/tex] y from y
∴ The vanilla cupcakes were left = y - [tex]\frac{2}{5}[/tex] y = [tex]\frac{3}{5}[/tex] y
∵ There are now 36 more vanilla cupcakes than chocolate
cupcakes
- Subtract [tex]\frac{1}{3}[/tex] x from [tex]\frac{3}{5}[/tex] y and equate the difference by 36
∴ [tex]\frac{3}{5}[/tex] y - [tex]\frac{1}{3}[/tex] x = 36
- Rearrange the terms in the left hand side
∴ - [tex]\frac{1}{3}[/tex] x + [tex]\frac{3}{5}[/tex] y = 36 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by [tex]\frac{1}{3}[/tex] to eliminate x
∴ [tex]\frac{1}{3}[/tex] x +
- Add equations (2) and (3)
∴ [tex]\frac{14}{15}[/tex] y = [tex]\frac{238}{3}[/tex]
- Divide both sides by [tex]\frac{14}{15}[/tex]
∴ y = 85
- Substitute the value of y in equation (1) to find x
∵ x + 85 = 130
- Subtract 85 from both sides
∴ x = 45
∵ [tex]\frac{1}{3}[/tex] chocolate cupcakes were left
∴ The chocolate cupcakes were left = [tex]\frac{1}{3}[/tex] × 45 = 15
∵ [tex]\frac{3}{5}[/tex] vanilla cupcakes were left
∴ The vanilla cupcakes were left = [tex]\frac{3}{5}[/tex] × 85 = 51
∴ The total number of cupcakes are left = 15 + 51 = 66
66 cupcakes are left in total
Learn more:
You can learn more about the system of equations in brainly.com/question/6075514
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