Sugar twist are 5.00lb. How many pounds cost $292.50.

Question

tarts costs $4.50 a pound. Sugar twists cost 5.00 a pound. Three times more pounds of sugar twists than tarts were sold. How many pounds of sugar twists were sold. The total cost was $292.50.

Answer 1

This is a systems of equations problem. We are given information to make 2 problems.

I'm going to call Sugar Twists X and Tarts Y for this.

 

We know that we sold 3 times more X than Y, so we can write

3x = y

 

We also know that in pricing, x = 4.50 and y = 5, and together they equal $292.50 so....

4.5y + 5x = 292.50

 

Now substitute y for 3x....

 

292.50 = 4.5(3x) + 5x

292.50 = 13.5x + 5x

292.50 = 18.5x

x = 15.81 (round to 15)

 

So now we know we sold 16 twists. We also know we sold 3 times more that tarts, so

15*3 = 45

Answer 2

I'm reading 'Three times more pounds of sugar twists than tarts were sold' to mean that the pounds of sugar twists are three times the pounds of tarts.  

 

Let T represent the number of tarts and S represent the number of sugar twists.    S is three times T since three times more pounds of sugar twists than tarts were sold.  S = 3T.  4.5T is the amount of money spent on tarts.  5S is the amount spent on sugar twists.  5S = 5(3T) = 15T.  The total amount spent is the amount spent on tarts, 4.5T, plus the amount spent on sugar twists, 5S or 15T.  

 

4.5T + 15T = 292.50

19.5T = 292.50

T = 292.50/19.5

T = 15 = 15 pounds of tarts were sold.

S = 3T = 45 pounds of sugar twists were sold.