Question

8 candles and 14 coupon books and earned AED 476. ]sells 8 candles and 9 coupon books and earned AED 346. Write and solve a system of equations to find the cost of a candle and a coupon book.

Answer 1

The cost of a candle is 14 AED and the cost of a coupon book is 26 AED.

Step-by-step explanation:

Let's assume the cost of a candle is x AED and the cost of a coupon book is y AED.

According to the given information:

1. 8 candles and 14 coupon books earned AED 476, so the equation will be:
   8x + 14y = 476
2. 8 candles and 9 coupon books earned AED 346, so the equation will be:
   8x + 9y = 346

To solve this system of equations, you can use the method of substitution or elimination.

Let's use the method of elimination:

1. Multiply the first equation by 9 and the second equation by 14 to make the coefficient of x the same in both equations:
   72x + 126y = 4284
   112x + 126y = 4844
2. Subtract the first equation from the second equation:
   40x = 560
3. Divide both sides of the equation by 40 to find the value of x:
   x = 14

Now, substitute the value of x into one of the original equations to find the value of y:

1. Using the first equation:
   8(14) + 14y = 476
2. Simplify:
   112 + 14y = 476
3. Subtract 112 from both sides:
   14y = 364
4. Divide both sides of the equation by 14:
   y = 26

Therefore, the cost of a candle is 14 AED and the cost of a coupon book is 26 AED.