Question

36) The ratio of Slade's stickers to Corbett's stickers is 5: 2. If Corbett
has 27 fewer stickers than Slade, how many stickers do they have
in all?

Answer 1

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:

$\frac{2}{5}~ =~\frac{x}{x~+~27}$

Cross multiply the system

$2~(x~+~27)~=~5~*~x$

Simplify by distributive property

$2~*~x~+~2~*~27~=~5x$

$2x~+~54~=~5x$

Subtract 2x on both sides

$2x~+~54~-~2x~=~5x~-~2x$

$54~=~3x$

Divide 3 on both sides

$54~/~3~=~3x~/~3$

${x=18}$

Add Corbett's and Slade's amounts together

Corbett = x = 18 stickers

Slade = x + 27 = 18 + 27 = 45 stickers

Total = 18 + 45 = $\Large\boxed{63~Stickers}$

Hope this helps!! :)

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Answer 2

Answer:

63 stickers

Step-by-step explanation:

Define the variables:

• Let x be the number of stickers Slade had.

• If Corbett has 27 fewer stickers than Slade:
  ⇒ Corbett = x - 27

Given ratio:

Slade : Corbett = 5 : 2

Substitute the defined variables:

$\implies \sf x : x - 27 = 5 : 2$

$\implies \sf \dfrac{x}{x-27}=\dfrac{5}{2}$

Cross multiply:

$\implies \sf 2x=5(x-27)$

Expand:

$\implies \sf 2x=5x-135$

Subtract 5x from both sides:

$\implies \sf -3x=-135$

Multiply both sides by -1:

$\implies \sf 3x=135$

Divide both sides by 3:

$\implies \sf x=45$

Therefore, Slade had 45 stickers.

Substitute the found value of x into the expression for the number of stickers Corbett had:

$\implies \sf 45-27=18$

Therefore, Corbett had 18 stickers.

Total number of stickers = 45 + 18 = 63