Question

a women bought some large frames for $17 each and some small frames for $9 each at a closeout sale. if she bought 19 frames for $219 , find how mant of each type she bought

Answer 1

Answer: Number of large frames: 6

Number of small frames: 13

Explanation:

In this problem, we can create a system of equations.

Let x be the number of large frames and y be the number of small frames.

Step 1: If in total there were 19 frames, we can create the equation: x+y=19

Step 2: Since a large frame is $17 each, we can say it is 17x. Similarly, the small frames would be 9y. The total price is $219, therefore, our second equation is 17x+9y=219.

Step 3: x+y=19

17x+9y=219

Step 4: To solve this system, we first have to find the value of either x or y.

We can use the first equation: y= -x+19

Step 5: Using this, we can substitute the value of y in our second equation. This would be 17x+ 9(-x+19)=219

Step 6: Now we solve for x: 17x-9x+171=219

8x=48; x=6

Step 7: Now that we have a number value for x, we can solve for y. We can substitute the value of x in the first equation: (6)+y=19

y=13

Step 8: Now we know the values of x and y so now we can find out how many of each type of frame she bought.

x= number of large frames= 6

y= number of small frames= 13