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Answer: 63 Stickers
Step-by-step explanation:
Given information:
Ratio = Slade : Corbett = 5 : 2
Corbett has 27 fewer stickers
Set variables:
Let x be the number of stickers Corbett has
Let x + 27 be the number of stickers Slade has
Set proportional equation:
[tex]\frac{2}{5}~ =~\frac{x}{x~+~27}[/tex]
Cross multiply the system
[tex]2~(x~+~27)~=~5~*~x[/tex]
Simplify by distributive property
[tex]2~*~x~+~2~*~27~=~5x[/tex]
[tex]2x~+~54~=~5x[/tex]
Subtract 2x on both sides
[tex]2x~+~54~-~2x~=~5x~-~2x[/tex]
[tex]54~=~3x[/tex]
Divide 3 on both sides
[tex]54~/~3~=~3x~/~3[/tex]
[tex]{x=18}[/tex]
Add Corbett's and Slade's amounts together
Corbett = x = 18 stickers
Slade = x + 27 = 18 + 27 = 45 stickers
Total = 18 + 45 = [tex]\Large\boxed{63~Stickers}[/tex]
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Answer:
63 stickers
Step-by-step explanation:
Define the variables:
Given ratio:
Slade : Corbett = 5 : 2
Substitute the defined variables:
[tex]\implies \sf x : x - 27 = 5 : 2[/tex]
[tex]\implies \sf \dfrac{x}{x-27}=\dfrac{5}{2}[/tex]
Cross multiply:
[tex]\implies \sf 2x=5(x-27)[/tex]
Expand:
[tex]\implies \sf 2x=5x-135[/tex]
Subtract 5x from both sides:
[tex]\implies \sf -3x=-135[/tex]
Multiply both sides by -1:
[tex]\implies \sf 3x=135[/tex]
Divide both sides by 3:
[tex]\implies \sf x=45[/tex]
Therefore, Slade had 45 stickers.
Substitute the found value of x into the expression for the number of stickers Corbett had:
[tex]\implies \sf 45-27=18[/tex]
Therefore, Corbett had 18 stickers.
Total number of stickers = 45 + 18 = 63