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3 years ago

Solve the equations 7x+9y=27 and 4x+5y=13 by combining the equations

Mathematics

1 answer:

Fantom [35]3 years ago

7 0

Is that what you need

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There are 2405 seats in the theatre. If the average cost is 250 for each seat, how much money is earned at one theatre event.

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4 years ago

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3 years ago

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the jurassic zoo charged $11 for each adult admission and $8 for each child. the total bill for the 195 people from a school tri

Otrada [13]

Children : 144

Adults : 51

Explanation

Step 1

Set the equations

let

x represents the number of children

y represents the number of adults

charge per child:8

charge per adult:11

total people:195

then

a)the total people is 195, so

$x+y=195\rightarrow equation(1)$

b) the total bill was $1713,so

total childrend +total adults=173

but,

total adults cost= rate*number of adults

total children cost= rate*number of childe

replacing

$8x+11y=1713\rightarrow equation(2)$

Step 2

solve the equations,

$\begin{gathered} x+y=195\rightarrow equation(1) \\ 8x+11y=1713\rightarrow equation(2) \end{gathered}$

a) isolate the x value from equation 81) and replace in eqaution (2)

$\begin{gathered} x+y=195\rightarrow equation(1) \\ \text{subtract y in both sides} \\ x+y-y=195-y \\ x=195-y \end{gathered}$

replace in equation (2)

$\begin{gathered} 8x+11y=1713\rightarrow equation(2) \\ 8(195-y)+11y=1713 \\ 1560-8y+11y=1713 \\ 3y+1560=1713 \\ \text{subtract 1560 in both sides} \\ 3y+1560-1560=1713-1560 \\ 3y=153 \\ \text{divide bothsides by 3} \\ \frac{3y}{3}=\frac{153}{3} \\ y=51 \end{gathered}$

therefore, the number of adults is 51

b) now, replace the y value into equation (1) to find x

$\begin{gathered} x+y=195\rightarrow equation(1) \\ x+51=195 \\ \text{subtract 51 in both sides} \\ x+51-51=195-51 \\ x=144 \end{gathered}$

so, the number of children is 144

I hope this helps you

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1 year ago