# Practical word question

#### debtless

Hi. I work out the answer in my head but of course the teacher wants to see my workings! Can someone please show me the equation to use?
Thanks

25 students go to a ball and total amount spent is $5500. Boys spend$100 each and girls spend $400 each. How many girls go to the ball? #### chiro MHF Helper Hey debtless. You should show what you have tried and think about it in terms of variables. To get you started you have three variables here - total amount, amount for boys and amount for girls. Boy and girls amounts are based on number of people and the amount per person. All up - you have five variables and you have to find some formula that links all of them together in some way. See if you can go further and tell me how you might try and do that - we can provide assistance if you show your attempts to do so. #### debtless OK so I tried the following but I can't seem to go in the right directions. 1. 5500 = b100 + b400 55 = b500 b = 55/500 b = 0.11 2. 25(b + 4b) = 5500 25b + 100b =5500 125b = 5500 b= 5500/125 b = 44 3. 25(b + (b+300))=5500 b + (b+300) = 5500/25 b + (b+300) = 220 2b + 300 = 220 2b = 220 -300 2b = - 80 b= -40 #### skeeter MHF Helper 25 students go to a ball and total amount spent is \$5500. Boys spend \$100 each and girls spend \$400 each. How many girls go to the ball?
Let $b$ = number of boys

$g$ = number of girls

$b+g=25$

$b(\$100) + g(\$400) = \$5500b=25-g \implies (25-g)(\$100) + g(\$400) = \$5500$

solve for $g$

#### DenisB

Or a shorter route (since you're doing it in your noggin'!):

g = girls : then boys = 25 - g

400g + 100(25 - g) = 5500 : solve for g

#### HallsofIvy

MHF Helper
Hi. I work out the answer in my head but of course the teacher wants to see my workings!