Answer:
dwafwfaffewaeawewae
Step-by-step explanation:
awew!
2 and 3/4 more cups of white flour are used than wheat flour.
5 x 3/4= 3 3/4
3 x 1/3= 1
3 3/4 - 1+ 2 3/4
Answer:
![\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}=2](https://tex.z-dn.net/?f=%5Cfrac%7B4p-3%7D%7B3p%2B1%7D%2B%5Cfrac%7B2p%2B5%7D%7B3p%2B1%7D%3D2)
Step-by-step explanation:
we are given
![\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}](https://tex.z-dn.net/?f=%5Cfrac%7B4p-3%7D%7B3p%2B1%7D%2B%5Cfrac%7B2p%2B5%7D%7B3p%2B1%7D)
we can see that
denominators of both terms are 3p+1
So, both has same denominators
so, we can combine numerators
and we get
![\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}=\frac{4p-3+2p+5}{3p+1}](https://tex.z-dn.net/?f=%5Cfrac%7B4p-3%7D%7B3p%2B1%7D%2B%5Cfrac%7B2p%2B5%7D%7B3p%2B1%7D%3D%5Cfrac%7B4p-3%2B2p%2B5%7D%7B3p%2B1%7D)
now, we can combine like terms
![\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}=\frac{4p+2p-3+5}{3p+1}](https://tex.z-dn.net/?f=%5Cfrac%7B4p-3%7D%7B3p%2B1%7D%2B%5Cfrac%7B2p%2B5%7D%7B3p%2B1%7D%3D%5Cfrac%7B4p%2B2p-3%2B5%7D%7B3p%2B1%7D)
![\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}=\frac{6p+2}{3p+1}](https://tex.z-dn.net/?f=%5Cfrac%7B4p-3%7D%7B3p%2B1%7D%2B%5Cfrac%7B2p%2B5%7D%7B3p%2B1%7D%3D%5Cfrac%7B6p%2B2%7D%7B3p%2B1%7D)
now, we can factor out common term
![\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}=\frac{2(3p+1)}{3p+1}](https://tex.z-dn.net/?f=%5Cfrac%7B4p-3%7D%7B3p%2B1%7D%2B%5Cfrac%7B2p%2B5%7D%7B3p%2B1%7D%3D%5Cfrac%7B2%283p%2B1%29%7D%7B3p%2B1%7D)
we can see that 3p+1 is on both top and bottom
so, we can cancel it
and we get
![\frac{4p-3}{3p+1}+\frac{2p+5}{3p+1}=2](https://tex.z-dn.net/?f=%5Cfrac%7B4p-3%7D%7B3p%2B1%7D%2B%5Cfrac%7B2p%2B5%7D%7B3p%2B1%7D%3D2)
One adult ticket costs £11 and one child ticket costs £8.5
Step-by-step explanation:
Let,
Adult ticket = a
Child ticket = c
According to given statement;
3a+4c=67 Eqn 1
5a+6c=106 Eqn 2
Multiplying Eqn 1 by 5;
![5(3a+4c=67)\\15a+20c=335\ \ \ Eqn\ 3](https://tex.z-dn.net/?f=5%283a%2B4c%3D67%29%5C%5C15a%2B20c%3D335%5C%20%5C%20%5C%20Eqn%5C%203)
Multiplying Eqn 2 by 3;
![3(5a+6c=106)\\15a+18c=318\ \ \ Eqn\ 4](https://tex.z-dn.net/?f=3%285a%2B6c%3D106%29%5C%5C15a%2B18c%3D318%5C%20%5C%20%5C%20Eqn%5C%204)
Subtracting Eqn 4 from Eqn 3
![(15a+20c)-(15a+18c)=335-318\\15a+20c-15a-18c=17\\2c=17\\](https://tex.z-dn.net/?f=%2815a%2B20c%29-%2815a%2B18c%29%3D335-318%5C%5C15a%2B20c-15a-18c%3D17%5C%5C2c%3D17%5C%5C)
Dividing both sides by 2
![\frac{2c}{2}=\frac{17}{2}\\c=8.5](https://tex.z-dn.net/?f=%5Cfrac%7B2c%7D%7B2%7D%3D%5Cfrac%7B17%7D%7B2%7D%5C%5Cc%3D8.5)
Putting c=8.5 in Eqn 1
![3a+4(8.5)=67\\3a+34=67\\3a=67-34\\3a=33](https://tex.z-dn.net/?f=3a%2B4%288.5%29%3D67%5C%5C3a%2B34%3D67%5C%5C3a%3D67-34%5C%5C3a%3D33)
Dividing both sides by 3;
![\frac{3a}{3}=\frac{33}{3}\\a=11](https://tex.z-dn.net/?f=%5Cfrac%7B3a%7D%7B3%7D%3D%5Cfrac%7B33%7D%7B3%7D%5C%5Ca%3D11)
One adult ticket costs £11 and one child ticket costs £8.5
Keywords: Linear equation, subtraction
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