Homework SourseA youth club held a pancake breakfast to raise money for a t
A youth club held a pancake breakfast to raise money for a trip. Tickets were $4 for kids and $7.50 for adults. If 282 tickets were sold and the group took in $1793, find the number of adults and the number of kids that attended the breakfast. Kids? Adults?
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Use a system of linear equations to solve the problem
Trish has two containers of water for a camping trip. one container holds 2 times as much as the other. The total amount of water is 27 gallons. how much water is in each container?
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Determine the number of solutions without graphing. (none, one, infinte)
8x+7y=8 7x+8y=8
Solution
1. Let the number of adults and the number of kids that attended the breakfast be x and y respectively. Then x+y = 282..(1) ( as 282 tickets were sold) and 4x+7.5 y = 1793 …(2)( as the group took in $1793).
On multiplying the 2nd equation by 2, we get 8x +15 y = 3586…(3).
On multiplying the 1st equation by 8, we get 8x+8y = 2256…(4).
Now, on subtracting the 4th equation from the 3rd equation, we get 8x+15y-8x-8y = 3586-2256 or, 7y = 1330 so that y = 1330/7 = 190. Now, on substituting y = 7 in the 1st equation, we get x+190 = 282 so that x = 282-190 = 92. Thus, the number of adults and the number of kids that attended the breakfast were 92 and 190 respectively.
2. Let the capacity of the smaller container be x gallons. Then, the capacity of the bigger container is 2x gallons. Now, since the total amount of water is 27 gallons, we have x+2x = 27 or, 3x = 27 so that x = 27/3 = 9. Then 2x = 2*9 = 18.
Thus, the capacity of the smaller container is 9 gallons and the capacity of the bigger container is 18 gallons.
3. We have 8x+7y = 8…(1) and 7x+8y = 8…(2) On multiplying the 1st equation by 7 and the 2nd equation by 8, we get 56x +49y = 56…(3) and 56x +64y = 64…(4). Now, on subtracting the 3rd equation from the 4th equation, we get 56x +64y-56x -49y = 64-56 or, 15y = 8 so that y = 8/15. Now, on substituting y = 8/15 in the 1st equation, we get 8x + 7*8/15 = 8 or, 8x = 8 -56/15 = 64/15. Hence x = (1/8)*64/15 = 8/15. Thus, there is a unique (one) solution, which is x = 8/15 and y = 8/15. We can verify the result by substituting these values of x and y in any of the 2 original equations.
