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anonymous

  • one year ago

pls help me with this its the last 2 days to turn in work and i dont know how Admission to the Pie Eating Contest is $1.50 for children and $4 for adults. On a certain day, 2200 people came to watch and $5050 is collected. How many children and adults attended the Contest? Show ALL work. Let x = number of children Let y = number of adults A. Write 2 equations to model this system: B. Solve the first equation for x (get the x alone on 1 side): 5 points C. Use Substitution to solve the equations and determine how many adults and how many children attended

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  1. Valpey
    • one year ago
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    Number of people (P = 2200) is equal to number of children (x) plus number of adults (y) so: P = x + y = 2200 Amount collected (A = $5050) is equal to the number of children times $1.50 plus the number of adults times $4. What does that equation look like?

  2. anonymous
    • one year ago
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    uhh....idk do i multiply ?

  3. anonymous
    • one year ago
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    can u help with part b and c pls thank u

  4. Valpey
    • one year ago
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    Try writing out an equation with x, y, $1.50, $4.00, and $5050. You can do it.

  5. anonymous
    • one year ago
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    uh x(1.50) * y(4.00)=5050 i really dont know how to :( i cant do it

  6. mathmate
    • one year ago
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    x(1.50) * y(4.00)=5050 is \(almost \) the same as: \(1.5x \color{red}{+} 4y=5050\) It is a plus because we add up the amounts received to get $5050.

  7. mathmate
    • one year ago
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    Can you find the second equation?

  8. mathmate
    • one year ago
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    oh, @Valpey already gave it to you as the first equation: x+y=2200 (meaning #children + #adults =2200 people)

  9. mathmate
    • one year ago
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    B. Solve the first equation for x (get the x alone on 1 side): This means that you need to isolate x from the first equation x+y = 2200

  10. anonymous
    • one year ago
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    x + y=2200 -1.5 -1.5=x ? .......

  11. mathmate
    • one year ago
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    You may want to concentrate on part B, which says: B. Solve the \(first\) equation for x (get the x alone on 1 side): This means that you need to \(isolate\) x from the first equation x+y = 2200 x=?

  12. anonymous
    • one year ago
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    x=1.5

  13. anonymous
    • one year ago
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    right?

  14. mathmate
    • one year ago
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    x+y=2200 subtract y from either side, what do you get?

  15. anonymous
    • one year ago
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    so substract 4from each side

  16. mathmate
    • one year ago
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    yes, subtract \(\color{red}{y}\) from each side of the equality sign!

  17. anonymous
    • one year ago
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    um so x+y=2200 -4 -4 like that ?

  18. mathmate
    • one year ago
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    y does not equal 4! Both x and y represent the number of people (children and adults) question says: " Let x = number of children Let y = number of adults " so we don't know y yet. y is an unknown representing the number of adults that we are trying to find. You have to subtract y as an entity, example x+y = 2200 so whatever y stands for, the following equations are still valid x+y-y=2200-y x=2200-y THis process is called isolating y because we have y only on the left-hand side.

  19. anonymous
    • one year ago
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    thank u

  20. anonymous
    • one year ago
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    thank u

  21. anonymous
    • one year ago
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    so in part c i would b making an equation out of the numbers and the variable right ?

  22. mathmate
    • one year ago
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    \(Example\) of substitution: given x+y=10 .......(1) 2x+3y=25.....(2) First isolate x: x=10-y.....(1A) Substitute means replace x (in the second equation) by the value of x in terms of y which we got from the first equation (1A) 2(10-y) + 3y = 25 .......(2A) Now solve (2A) to get the value of y: 1. distribute 2*10 - 2y + 3y = 25 group like terms, and isolate y 3y-2y +20-20 = 25-20 y =5 Now, backsubstitute value of y into the first equation (1) to solve for x: x+5 = 10 x = 10 - 5 x=5 You would proceed the same way to work on part C.

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