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Applications if system of equation

(1) Maggie's ma tells everyone that she is 14years younger than she actually is.if you add her actual age to the age that she tells people she is,the total is 122. What is the actual age of Maggie's ma(as reported by bob Dylan)?

(2)A movie theater charges $9.50 for an adult and 7.75 for a child to see a movie.if 92 people were at the 9.20 PM show and the total admission paid was $837.25, How many adults were at the movie?
(3)An oil painting is in the shape of a rectangle.The perimeter of the painting is 127.4 inches, and the lenght of the painting is 1.6 times the width of the painting.Find the dimensions of the painting.

(4)Maria invested $5500 in two mutual funds.One fund earned an 8% profit,while the other earned a 1.5% profit.Between the two accounts,Maria made a profit of $180. How much was invested in each account?

(5) Raheem can buy peanuts for $0.40 per pound and cashews for $1.05 per pound.How many pounds of each type should he buy to produce 120 pounds of a mixture that costs him $0.66 per pound?

1 Answer by Expert Tutors

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JERRY M. | Ton bon ami! JerryTon bon ami! Jerry
1) X represents her actual age and Y represents the age she pretends to be.
    the first equation is: x - 14 =y
    the second one is :  x + y = 122
    In the second equation, replace y by (x-14) and solve the equation.
    Her actual age is 68 years old because x=68
2)  X represents adult and Y represents child
     The first equation is      : X + Y =92
      The second equation is: 9.5X + 7.75Y = 837.25
      Replace Y by (92 - X) in the second equation
      The second equation will be : 9.5X + 7.75(92-X) = 837.25
     The last step is to solve the equation
      X = 71. it means that there were 71 adults at the movie.
3) Perimeter = 127.4 Lenght = 1.6W
Perimeter= 2L + 2W
127.4 = 2(1.6W) + 2W
127.4 = 3.2W + 2W
127.4 = 5.2 W
24.5 = Width
1.6 * 24.5 = Length
39.2 = L