# 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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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,
$1.10x+3.60y=\left(x+y\right)1.85$
Simplify this equation.
$1.10x+3.60y=1.85x+1.85y$
$0.75x-1.75y=0$
Multiply the equation by 100 to eliminate decimals.
$100\left(0.75x-1.75y\right)=100\left(0\right)$
2) $75x-175y=0$
Step 3
Multiply equation (1) by 75 and subtract equation (2) from equation (1).
$75x+75y=3750$
$75x-175y=0$
$\left(-\right)\left(+\right)=\left(-\right)$
$250y=3750$
$y=\frac{3750}{250}$
$y=15$
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.