answer please to help me

Question

Bill and Mary Ann went to the Viola bakery. Bill bought 4 danishes and 8 filled donuts for ​$15.28. Mary Ann bought 6 of each for ​$13.32. What is the price of each type of​ pastry?

Answer 1

Let D = cost of one Danish (in cents)

Let F = cost of one Filled donut (in cents).

Then 4D + 8F = 1528 (note that $15.28 has been converted to pennies)

6D + 6F = 1332

At this point you can try some sort of addition/elimination, but check to see if the equations can be simplified to allow working with smaller numbers. Note that every term of the first equation is divisible by 4. Similarly every term of the 2nd equation is evenly divisible by 6.

D + 2F = 382

D + F = 222

Now subtract the 2nd equation from the 1st to eliminate D:

F = 160 (or $1.60).

So, D = 222 - 160 = 62 (or $0,62).

Check cost to Bill:

4D = $2.48

8F = $12.80

Cost to Bill = $15.28 (check)