Answer the following mathematical questions

Question

1) Molly and Jason were selling in a cake sale. After Molly sold 5/7 of her brownies, she had 2/3 as many brownies as Jason. Jason then sold 40 brownies and had a quarter as many as Molly. How many did each of them have at first? 

 

2) The ratio of the area of the shaded to the unshaded portions in a rectangle ABEG is 5:3. The ratio of the area of triangle BCE to triangle AFG is 3:2. The area of ABEG is 152cm2 . The area of triangle CDE is 1/4 of the area of ABEG . find the difference between the area of the shaded portions and unshaded portions of the figure.   

 

 

Answer 1

1)  Let M = the number of brownies that Molly started with and J = the number Jason started with.  We have 2 unknowns (M and J) so we need 2 equations relating the unknowns to solve for them.

 

After Molly sold 5/7 of her brownies (leaving her with 1 - 5/7 = 2/7 left), she had 2/3 as many brownies as Jason

 

(2/7)M = (2/3)J

 

Jason then sold 40 brownies and had a quarter as many as Molly.

 

J - 40 = (1/4)(2/7)M            [Remember, Molly only has 2/7 of her brownies left]

 

Let's use the first equation to substitute (2/3)J in place of (2/7)M in the second equation and solve for J:

J - 40 = (1/4)(2/7)M            [Second equation]

J - 40 = (1/4)(2/3)J             [Substituted (2/3)J in place of (2/7)M]

J - 40 = (1/6)J

(5/6)J = 40

 

J = 48

 

Solve for M:

(2/7)M = (2/3)J

M = (7/3)J

M = (7/3)(48) = 112

 

2)  To solve the second problem, we need to see a diagram of the figures.