Answer:
$490
Step-by-step explanation:
Shauna spent $175 on a pair of shoes.
She spent 1/9 of the remaining money on a shirt.
If he still had 4/7 of his money left,how much did he have at first ?
Solution:
Let at first, Shauna have = ![x](https://tex.z-dn.net/?f=x)
Money spent on a pair of shoes = $175
Remaining money = ![x-175](https://tex.z-dn.net/?f=x-175)
<u>As she spent 1/9 of the remaining money on a shirt.</u>
Money spent on shirt = ![\frac{1}{9} \times(x-175)=\frac{x}{9} -\frac{175}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B9%7D%20%5Ctimes%28x-175%29%3D%5Cfrac%7Bx%7D%7B9%7D%20-%5Cfrac%7B175%7D%7B9%7D)
As he still had
of his money left:-
Money left = ![\frac{4}{7}\ of\ his\ money=\frac{4x}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B7%7D%5C%20of%5C%20his%5C%20money%3D%5Cfrac%7B4x%7D%7B7%7D)
Money left with Shauna = Total money, she had at first -(Money spent on a pair of shoes + Money spent on shirt )
![\frac{4x}{7} =x-(175+{\frac{x}{9} -\frac{175}{9} )\\\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B4x%7D%7B7%7D%20%3Dx-%28175%2B%7B%5Cfrac%7Bx%7D%7B9%7D%20-%5Cfrac%7B175%7D%7B9%7D%20%29%5C%5C%5C%5C%5C%5C)
![\frac{4x}{7} =x-(\frac{175}{1} -\frac{175}{9} +\frac{x}{9} )\\\\ \frac{4x}{7} =x-(\frac{1575-175}{9} +\frac{x}{9} )\\\\ \frac{4x}{7}=x-(\frac{1400}{9} +\frac{x}{9} )\\ \\ \frac{4x}{7}=x-\frac{1400}{9} -\frac{x}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%7D%7B7%7D%20%3Dx-%28%5Cfrac%7B175%7D%7B1%7D%20-%5Cfrac%7B175%7D%7B9%7D%20%2B%5Cfrac%7Bx%7D%7B9%7D%20%29%5C%5C%5C%5C%20%5Cfrac%7B4x%7D%7B7%7D%20%3Dx-%28%5Cfrac%7B1575-175%7D%7B9%7D%20%2B%5Cfrac%7Bx%7D%7B9%7D%20%29%5C%5C%5C%5C%20%5Cfrac%7B4x%7D%7B7%7D%3Dx-%28%5Cfrac%7B1400%7D%7B9%7D%20%2B%5Cfrac%7Bx%7D%7B9%7D%20%29%5C%5C%20%5C%5C%20%5Cfrac%7B4x%7D%7B7%7D%3Dx-%5Cfrac%7B1400%7D%7B9%7D%20-%5Cfrac%7Bx%7D%7B9%7D)
Subtracting both sides by
and adding both sides by ![\frac{x}{9}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B9%7D)
![\frac{4x}{7} -x+\frac{x}{9} =-\frac{1400}{9} -x+\frac{x}{9} +x-\frac{x}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%7D%7B7%7D%20-x%2B%5Cfrac%7Bx%7D%7B9%7D%20%3D-%5Cfrac%7B1400%7D%7B9%7D%20-x%2B%5Cfrac%7Bx%7D%7B9%7D%20%2Bx-%5Cfrac%7Bx%7D%7B9%7D)
Taking LCM of 7 and 9, we get 63
![\frac{36x-63x+7x}{63} =-\frac{1400}{9} \\ \\ -\frac{20x}{63}=-\frac{1400}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B36x-63x%2B7x%7D%7B63%7D%20%3D-%5Cfrac%7B1400%7D%7B9%7D%20%5C%5C%20%5C%5C%20-%5Cfrac%7B20x%7D%7B63%7D%3D-%5Cfrac%7B1400%7D%7B9%7D)
Adding both side by -
![\frac{36x-63x+7x}{63} =-\frac{1400}{9} \\ \\ \frac{20x}{63}=\frac{1400}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B36x-63x%2B7x%7D%7B63%7D%20%3D-%5Cfrac%7B1400%7D%7B9%7D%20%5C%5C%20%5C%5C%20%5Cfrac%7B20x%7D%7B63%7D%3D%5Cfrac%7B1400%7D%7B9%7D)
By cross multiplication:
![20x\times9=1400\times63\\180x=88200\\](https://tex.z-dn.net/?f=20x%5Ctimes9%3D1400%5Ctimes63%5C%5C180x%3D88200%5C%5C)
Dividing both sides by 180
![x=490](https://tex.z-dn.net/?f=x%3D490)
Therefore, total $490, she had at first.