This question comes from my overseas niece's homework. I suspect the question is wrong.
Here it goes:
200php bills = x
500php bills = y
1000php bills = z
z = 2x
y = z - 5
substitute z-value:
y = 2x - 5
200x + 500y + 1000z = 30,000
Substitute to get all in terms of x:
200x + 500(2x-5) + 1000(2x) = 30,000
Distribute:
200x + 1000x - 2500 + 2000x = 30,000
Combine like terms:
3200x - 2500 = 30,000
Add 2500 to both sides:
3200x = 32,500
divide both sides by 3200:
x = 10.15625
# of bills needs to be a whole number...
So I put it into excel, and using the first 2 equations with only whole numbers of bills, I get can totals of 29,800 and 31,700, but not 30,000.
Here it goes:
Here's what I got:Denise organized a fund raising project to help calamity victims. She collected a total of 30,000Php consisting 200Php, 500 php and 1000Php Bills. The number of 200 is twice the number of 1000 and the number of 500 is five less than the number of 1000. How many of each bill did she have?
200php bills = x
500php bills = y
1000php bills = z
z = 2x
y = z - 5
substitute z-value:
y = 2x - 5
200x + 500y + 1000z = 30,000
Substitute to get all in terms of x:
200x + 500(2x-5) + 1000(2x) = 30,000
Distribute:
200x + 1000x - 2500 + 2000x = 30,000
Combine like terms:
3200x - 2500 = 30,000
Add 2500 to both sides:
3200x = 32,500
divide both sides by 3200:
x = 10.15625
# of bills needs to be a whole number...
So I put it into excel, and using the first 2 equations with only whole numbers of bills, I get can totals of 29,800 and 31,700, but not 30,000.