can someone tell me how to work this question out? need to know for exam.
A drink stall sells small,medium and large cups of fruit drink for $1.50, $2.00 and $2.50. in one morning three times as many medium cups were sold as small cups, and the number of large cups sold was 140 less than the number of meduim cups. if the total drink sales was $1360, how many of each size cup was sold?
The drink stall sells small cups of fruit drink for $1.5, medium sized cups for $2 and large cups for $2.5.
On the day under consideration they sold 3 times as many medium sized cups as they sold small cups. If the number of small cups sold is S, the number of medium sized cups is 3*S. The number of large cup was 140 less than the number of medium sized cups or 3*S - 140.
The total sales is 1.5*S + 2*3*S + 2.5*(3*S - 140). This is equal to $1360.
1.5*S + 2*3*S + 2.5*(3*S - 140) = 1360
=> 1.5*S + 6*S + 7.5*S - 350 = 1360
=> 15S = 1360 + 350
=> 15S = 1710
=> S = 1710/15
=> S = 114
The number of medium cups sold is 3*114 = 342 and the number of large cups sold is 342 - 140 = 202.
The stall sold 114 small cups, 342 medium cups and 202 large cups.
Let S, M and L stand for small, medium and large.
So S(1.5) + M(2) + L(2.5) = 1360. This means each size cup times its price, all added together equals the entire amount of $1360.
But you can't solve with three different variables, so you have to get everything so you only have one variable. Let's see what you know:
3S=M 3 times as many medium drinks as small or, turning it around, 1/3M=S.
L= M-140 Number of large cups is 140 less than the number of medium
Now, plugging in: 1/3M(1.5) + M(2) + (M-140)(2.5) = 1360.
By working out the value of M mathematically, you will know how many medium cups were sold. 1/3 of that number will be the number of small cups, and the number of Medium - 140 will give you the number of large cups.