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2 years ago

Please show your work

Mathematics

1 answer:

White raven [17]2 years ago

3 0

Let a,b & c be the number of cookies Adrian, Bobby and Calvin baked respectively.

(a+b+c)/3 =138

(a+b)/2 =136

a+b=272

a=272-b

(b+c)/2 =125

b+c=250

c=250-b

Sub a=272-b and c=250-b into (a+b+c)/3 =138,

(a+b+c)/3 =138

[(272-b)+b+(250-b)]/3 = 138

272-b+b+250-b = 414

-b = -108

b=108

From the above,

a=272-b

=272-108

a=164

c=250-b

=250-108

c=142

∵ a=164

b=108

c=142

∴ Adrian baked 164 cookies.

Bobby baked 108 cookies.

Calvin baked 142 cookies.

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Find the value of x and y

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Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

What does the information want:

value of x
value of y

Let's gather some information:

ΔA'BC' and ΔABC are similar triangles

⇒ Angle B is shared by both triangles

⇒ Angle A' and A are the same, as they are both on parallel

lines, A'C' and AC, and both angles are formed with the

same line AB

⇒ by the Angle-Angle Theorem*, they are similar triangles

If they are similar triangles:

⇒ their side lengths are proportional to each other

let's find x's value

⇒ let's set up a proportion

$\frac{A'B}{AB} =\frac{A'C'}{AC} \\\frac{30}{x+30} =\frac{14}{22} \\14(x+30) = 30*22\\14x + 420 = 660\\14x = 240\\x = 17.143$

let's find y's value

⇒ let's set up a proportion

$\frac{BC'}{BC} =\frac{A'C'}{AC} \\\frac{y}{y+15} =\frac{14}{22} \\22y=14(y+15)\\22y=14y+210\\8y=210\\y=26.25$

Answer:

x= 17.143
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Hope that helps!

#LearnwithBrainly

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