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o-na [289]
3 years ago
7

Walter has 124 bills consisting of 5 dollar bills and 10 dollar bills. If his total amount of money is $840, how many bills of e

ach does he have?
Mathematics
1 answer:
Romashka [77]3 years ago
8 0
For this question here are the formulas,
Let T be the number of 10's
Let F be the number  5's

Let us find the 10's first by this formula.
<span>5(124 - T) + 10T = 840
</span>620-5T + 10T = 840
then
5T = <span>220
</span>5        5

T=44
<span>Now let's find the F using this formula.
</span>
5F + 10T = 840
Sustitute T 
5F + 10(44) = 840
<u>5F</u> = <u>400
</u>5         5
F = 80

to Check 
F + T = 124
80 + 44 = 124

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MN is a diameter of a circle with centre ' O ' . If BD = CD , prove that ∠OAD = ∠OCD
Varvara68 [4.7K]

Answer:

\sf \: Proved \: \angle \: OAD  \:  =  \angle \: OCD

Step-by-step explanation:

<em>Given:</em>

Mn is diameter of circle having centre O

and BD = OD,

<em><u>To prove that:</u></em>

<u>\angle \: OAD  \:  =  \angle \: OCD</u>

<em>Solution:</em>

Join the points O and B and draw OB,

On joining the line,

in ∆OCD and ∆OBD,

OC =OB → (Radius of same circle)

BD =CD → (from given)

OD =OD → (Common side in both the triangles)

Hence ∆OCD and ∆OBD are congruent from SSS property.

so we can say that,

\angle \: OBD  \:  =  \angle \: OCD

Consider above prove as statement A

Corresponding angles of congruent traingle.

in ∆ OAB,

OA = OB (radius of same circle)

hence ∆OAB is an isosceles traingle.

We know that opposite angle of isosceles traingle are always equal. hence,

\angle \: OBD  \:  =  \angle \: OAB \\ \angle \: OAB  \:  =  \angle \: OAD (same \: angles) \\ \angle \: OBD  \:  =  \angle \: OAD

Consider above prove as statement B

From Statement A & B we can say that

\angle \: OAD  \:  =  \angle \: OCD

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add them all up which is 40 then divide by the amount of numbers there are. in this case 5, so 40 ÷ 5 = 8

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Answer:

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Step-by-step explanation:

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