v Check your answer 1 point 18 Barbara bought 43 stamps at t

v. Check your answer (1 point). 18) Barbara bought 43 stamps at the post office. Some were $0.35 stamps, and the rest were $0.48 stamps If the total cost of the stamps was $17, how many of each type of stamp did she buy? 19) Anne and Nancy use a metal alloy that is 19% copper to make jewelry. How many ounces of a 12% copper alloy must be mixed with a 25% copper alloy to form 65 ounces of the desired 19% copper alloy?

Solution

20.) Let the price of each package of chocolate chip dough and gingerbread dough be $ x and $ y respectively. Phil sold 8 packages of chocolate chip dough and 5 packages of gingerbread dough for $ 206. Therefore, we have 8x + 5y = 206…(1). Sean sold 2 packages of and 3 packages of gingerbread dough for $ 76. Therefore, 2x + 3y = 76… (2). On multiplying both the sides of the 2nd equation by 4 , we have 8x + 12y = 304… (3). Now, on subtracting the 1^st equation from the 3^rd equation, we have 8x + 12y – 8x – 5y = 304 – 206 or, 7y = 98. Therefore, y = 98/7 = 14. Now, on substituting y = 14 in the 2^nd equation, we get 2x + 3*14 = 76 or, 2x = 42 = 76, or, 2x = 76 – 42 = 34. Therefore, x = 34/2 = 17. Thus the price of each package of chocolate chip dough is $ 17 and the price of each package of gingerbread dough is $ 14. We can verify this result by substituting these values of x and y in the 1^st equation.

21) Let us call these cars A and B and let the speed of car A be x kph. Then the speed of car B is x -15 kph. In 6 hours, car A travels 6x km and car B travels 6 (x - 15) km. Since the cars A and B are travelling in opposite directions and since in 6 hours, these two cars are 510 km apart, hence the total distance travelled by car A and B together, in 6 hours, is 510 km. therefore, we have 6x + 6(x – 15) = 510 or, 6x + 6x – 90 = 510 or, 12x = 510 + 90 = 600. Therefore, x = 600/12 = 50. Then x – 15 = 50 – 15 = 35 Thus the two cars are travelling at the speeds of 50 kph and 35 kph respectively.