A restaurant mixes sugar and cinnamon together to sprinkle on desserts. The cost of sugar is $1.10 kg and the cost of cinnamon is $3.60 kg What mass of each is needed to make 50 kg of mixture that costs $1.85 kg. Solve using elimination.

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timbalemX · Accepted Answer

Step 1 Consider a restaurant which mixes sugar and cinnamon to sprinkle on deserts. The cost of sugar is given to be $1.10 kg cost of cinnamon is given to be ​​​​​​​$3.60 kg The objective of the problem is to find the mass that is required to make 50 kg of mixture which could costs ​​​​​​​$1.85 kg Step 2 Let x be the mass of sugar required and y be the mass of the cinnamon required. Since 50 kg of mixture is required, the first equation is, 1) x+y=50 A total mixture of 50 kg costing ​​​​​​​$1.85 kg is required. So, the second equation is, 1.10x+3.60y=(x+y)1.85 Simplify this equation. 1.10x+3.60y=1.85x+1.85y 0.75x−1.75y=0 Multiply the equation by 100 to eliminate decimals. 100(0.75x−1.75y)=100(0) 2) 75x−175y=0 Step 3 Multiply equation (1) by 75 and subtract equation (2) from equation (1). 75x+75y=3750 75x−175y=0 (−)(+)=(−) 250y=3750 y=3750250 y=15 Substitute y=15 in equation (1) to find x. x+15=50 x=50−15 x=35 Therefore, 35 kg of sugar and 15 kg of cinnamon is required to make a mixture of 50kg.

A restaurant mixes sugar and cinnamon together to sprinkle on desserts. The cost of sugar is $1.10/kg and the cost of cinnamon is $3.60/kg.What mass of each is needed to make 50 kg of mixture that costs $1.85/kg?

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