Respuesta :
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 = [tex]x[/tex]
Money spent on a pair of shoes = $175
Remaining money = [tex]x-175[/tex]
As she spent 1/9 of the remaining money on a shirt.
Money spent on shirt = [tex]\frac{1}{9} \times(x-175)=\frac{x}{9} -\frac{175}{9}[/tex]
As he still had [tex]\frac{4}{7}[/tex] of his money left:-
Money left = [tex]\frac{4}{7}\ of\ his\ money=\frac{4x}{7}[/tex]
Money left with Shauna = Total money, she had at first -(Money spent on a pair of shoes + Money spent on shirt )
[tex]\frac{4x}{7} =x-(175+{\frac{x}{9} -\frac{175}{9} )\\\\\\[/tex]
[tex]\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}[/tex]
Subtracting both sides by [tex]x[/tex] and adding both sides by [tex]\frac{x}{9}[/tex]
[tex]\frac{4x}{7} -x+\frac{x}{9} =-\frac{1400}{9} -x+\frac{x}{9} +x-\frac{x}{9}[/tex]
Taking LCM of 7 and 9, we get 63
[tex]\frac{36x-63x+7x}{63} =-\frac{1400}{9} \\ \\ -\frac{20x}{63}=-\frac{1400}{9}[/tex]
Adding both side by -
[tex]\frac{36x-63x+7x}{63} =-\frac{1400}{9} \\ \\ \frac{20x}{63}=\frac{1400}{9}[/tex]
By cross multiplication:
[tex]20x\times9=1400\times63\\180x=88200\\[/tex]
Dividing both sides by 180
[tex]x=490[/tex]
Therefore, total $490, she had at first.
