John bought 7 bags of cement and 3 bags of gravel with the total weight of 215kgs. Shona bought 5 bags of cement and 4 bags of gravel with the total weight of 200kgs. How much does 1 bag of cement weigh and how much does 1 bag of gravel weigh?
Step 1: Write down the information we got in a simplified form => cement (c) .... 7 bags .... 5 bags, gravel (g) ...... 3 bags .... 4 bags, total weight .. 215kgs ... 200kgs ... Step 2: Transfer into 2 equations, one for each person => 7c + 3g = 2155c + 4g = 200 Step 3: Make c the subject of the first equation => c = (215 - 3g) : 7 Step 4: Substitute into the second equation and solve for g. => 5 x [(215 - 3g) : 7] + 4g = 200 ... (multiply by 7)... 5 x (215 - 3g) + 28g = 1400 ... 1075 - 15g + 28g = 1400 ... 13g = 325 ... (divide by 13)... g = 25 -> One bag of gravel weighs 25kgs. ... Step 5: Substitute for g into c = (215 - 3g) : 7 and solve for c. => c = (215 - 3 x 25) : 7 ... c = (215 - 75) : 7 ... c = 140 : 7 ... c = 20 -> One bag of cement weighs 20kgs.
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