Mrs Tan bought 4 times as many pens as notebooks and each notebook cost $8.20 more than each pen. She spent $26 more on the book s than the pens. Mrs Tan spent $394 altogether on the pond and notebooks, how much was the cost of a notebook?
1 answer:
Let x be the cost of 1 pen then cost of 1 notebook = x + 8.20 Let y be the number of pens Tan buys then number of notebooks Tan buys = y/4 She spent $26 more on books than on pens which means Cost of notebooks - Cost of pens = 26 (x + 8.20) * y/4 - xy = 26 Sinplifying it (xy + 8.20y)/4 - xy = 26 (xy + 8.20y - 4xy)/4 = 26 8.20y - 3xy = 104 She spent $394 which means Cost of notebooks + Cost of pens = 394 (x + 8.20) * y/4 + xy = 394 Simplifying it (xy + 8.20y)/4 + xy = 394 (xy + 8.20y + 4xy)/4 = 394 8.20y + 5xy = 1576 Now, we have two equations, (1) 8.20y - 3xy = 104 (2) 8.20y + 5xy = 1576 Now we need to find a third equation with either x or y as the subject of any of both the previous equations. Let's make y the subject of (2) equation 8.20y + 5xy = 1576 y(8.20 + 5X) = 1576 (3) y = 1576/(8.20 + 5x) Let's substitute the new value of y from (3) into (1) because we rearranged (2) to from (3) 8.20y - 3xy = 104 y(8.20 - 3x) = 104 y = 104/(8.20 - 3x) 1576/(8.20 + 5x) = 104/(8.20 - 3x) 1576 * (8.20 - 3x) = 104 * (8.20 + 5x) 12923.2 - 4728x = 852.8 + 520x 12923.2 - 852.8 = 4728x + 520x 12070.4 = 5248x 12070.4/5248 = x x = 2.3 Now find the value of y by substituting the value of x in either equation, preferably (3) y = 1576/(8.20 + 5x) y = 1576/(8.20 + 5 * (2.3)) y = 80 Therefore cost of 1 notebook = x + 8.20 = 2.3 + 8.20 = $10.50
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