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?

sibuzwaW 2021-08-09 Answered
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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Expert Answer

timbalemX
Answered 2021-08-10 Author has 108 answers

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
0.75x1.75y=0
Multiply the equation by 100 to eliminate decimals.
100(0.75x1.75y)=100(0)
2) 75x175y=0
Step 3
Multiply equation (1) by 75 and subtract equation (2) from equation (1).
75x+75y=3750
75x175y=0
()(+)=()
250y=3750
y=3750250
y=15
Substitute y=15 in equation (1) to find x.
x+15=50
x=5015
x=35
Therefore, 35 kg of sugar and 15 kg of cinnamon is required to make a mixture of 50kg.

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