a) 2 pounds of Sour Patch Kids
b) 3 pounds of Rolos
Step-by-step explanation:
Given,
Pounds of candy bought = 5 pounds
Cost of sour patch per pound = $2.25
Cost of Rolos per pound = $1.75
Total amount spent = $9.75
Let,
x = Number of pounds of sour patch
y = Number of pounds of rolos
x+y=5
x = 5-y Eqn 1
2.25x+1.75y=9.75 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
![2.25(5-y)+1.75y=9.75\\11.25-2.25y+1.75y=9.75\\11.25-0.5y=9.75\\11.25-9.75=0.5y\\1.50=0.5y\\0.5y=1.50](https://tex.z-dn.net/?f=2.25%285-y%29%2B1.75y%3D9.75%5C%5C11.25-2.25y%2B1.75y%3D9.75%5C%5C11.25-0.5y%3D9.75%5C%5C11.25-9.75%3D0.5y%5C%5C1.50%3D0.5y%5C%5C0.5y%3D1.50)
Dividing both sides by 0.5
![\frac{0.5y}{0.5}=\frac{1.50}{0.5}\\y=3\\](https://tex.z-dn.net/?f=%5Cfrac%7B0.5y%7D%7B0.5%7D%3D%5Cfrac%7B1.50%7D%7B0.5%7D%5C%5Cy%3D3%5C%5C)
Putting y = 3 in Eqn 1
![x=5-3\\x=2](https://tex.z-dn.net/?f=x%3D5-3%5C%5Cx%3D2)
a) 2 pounds of Sour Patch Kids
b) 3 pounds of Rolos
Keywords: linear equations, substitution method
Learn more about substitution method at:
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