math

[Bess]

For the new year, Mr. He simply spent 9/4 times more on gifts than his budget predicted.
He spent 405 euros.
His wife, Mrs. Simple spent 8/5 times more on gifts than he had anticipated.
She spent 5 euros less than Mr. Simple.
a) what was the total budget for the gifts from Mr. Simple and Mrs. Simple?
b) how much did they exceed the foreseen budget?

 

[lev888]

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[HallsofIvy]

For the new year, Mr. He simply spent 9/4 times more on gifts than his budget predicted.
He spent 405 euros.
His wife, Mrs. Simple spent 8/5 times more on gifts than he had anticipated.
She spent 5 euros less than Mr. Simple.
a) what was the total budget for the gifts from Mr. Simple and Mrs. Simple?
b) how much did they exceed the foreseen budget?

I have a problem with the grammar here! "He simply spent 9/4 times more on gifts" means that if he planned to spend "x" then he spent x+ (9/4)x= (13/4)x. But I suspect you meant he spent 9/4 as much as he planned- (9/4)x, not (13/4)x.

If I am correct then (9/4)x= 405 so x= (4/9)(405)= 1520/9 Euros.

Mrs. Simple spent 8/5 as much as planned, then taking y to be the amount planned (8/5)y= 400 (5 less than 405) so y= (5/8)(400)= 250 Euros.

I presume you can now find the sum and the difference from the 805 Euros planned.

 

[HallsofIvy]

If it really was 9/4 and 8/5 more, 1+ 9/4= 13/4 and 1+ 8/5= 13/5 then (13/4)x= 405 so x= (4/13)(405) and y= (5/13)(400).