Answer:
donuts cost $1.5
danishes cost $1.57
Step-by-step explanation:
This is a typical 2-equation syestem with 2 unknown variables problem. Lets find out which are our equations and unknowns.
Bill ought 3 danishes and 8 filled donuts for $14.67. Lets call d the price of donuts and c the price of danishes. We can then write Bill expenditures as an equation (I will omit $ symbol for simplicity):
3 c + 8 d = 14.67 [eq 1]
Now we can do the same for Mary's expenditures, as she bought 7 of each for $16.73:
7 c + 7 d = 16.73 [eq. 2]
Now, lets take eq. 1 and try to get the value of one of the variables, for example c, as function of the other -in this case, d. Notice you could also do this with eq. 2.
So:
3 c + 8 d = 14.67
Subtract 8d in both sides:
3c = 14.67 - 8d
Now, divide both sides by 3:
c = (14.67 - 8d)/3
So, we have c in function of d. Now, replace this value in eq 2:
7*(14.67 - 8d)/3 + 7 d = 16.73
(7/3)*(14.67 - 8d) + 7d = 16.73
Applying distributive:
(7/3)*14.67 - (7/3)*8d + 7d = 16.73
34.23 - 18.67d + 7d = 16.73
34.23 - 11.67d = 16.73
Now, subtract 34.23 in both sides:
-11.67 d = -17.5
Dividing both sides by -11.67
d = 1.50
So, every donuts costs $1.5. If we replace this value in any of the equations of the system we get c. Lets replace in eq. 1:
3 c + 8 d = 14.67
3 c + 8*1.5 = 3c + 12 = 14.67
Subtract 12 in both sides:
3c = 4.67
Divide by 3 in both sides:
c = 1.57
Important: notice that the results may variate in some decimals or less depending on how many numbers after the coma you use. For example, d is really 1.49957155098543 but I used 1.50, if you are more precise and use 1.49957 you results may variate a little but not significantly.
So, c=1.57 and d=1.50 is the solution. A donuts cost $1.5 and a danish $1.57.
