Answer:

1.d. compound-complex

Explanation:

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SUBSTITUTION

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\large \bold{\blue{Problem:}}Problem: A collection of 5 pesos and 1 peso coins totals 202 pesos the total number of coins Is 50 how many of each kind are there?

» Let's assign variables to each coins, let (x) be the total number of 5 peso coins and (y) as the total number of 1 peso coins.

Since (x) is 5 peso, multiply it to five, same as (y) multiplied to one totaling 202 pesos.

The sum of (x) and (y) is 50 since the total number of coins is 50

\begin{gathered} \begin{cases} \sf 5x + 1y = 202 \\ \sf x + y = 50 \end{cases} \begin{array}{l}\red{(eq.1)} \\ \red{(eq.2)} \end{array}\end{gathered}

{

5x+1y=202

x+y=50

(eq.1)

(eq.2)

» Solve for (x) by substituting (y) to equation 1:

\begin{gathered} \begin{cases} \sf 5x + 1y = 202 \\ \sf y = 50 - x \end{cases} \end{gathered}

{

5x+1y=202

y=50−x

\begin{gathered} \begin{cases} \sf 5x + (50 - x) = 202 \\ \sf y = 50 - x \end{cases} \end{gathered}

{

5x+(50−x)=202

y=50−x

\begin{gathered} \begin{cases} \sf 5x + 50 - x = 202 \\ \sf y = 50 - x \end{cases} \end{gathered}

{

5x+50−x=202

y=50−x

\begin{gathered} \begin{cases} \sf 5x - x= 202 - 50 \\ \sf y = 50 - x \end{cases} \end{gathered}

{

5x−x=202−50

y=50−x

\begin{gathered} \begin{cases} \sf 4x= 152 \\ \sf y = 50 - x \end{cases} \end{gathered}

{

4x=152

y=50−x

\begin{gathered} \begin{cases} \sf \frac{ \cancel4x}{ \cancel4} = \frac{152}{4} \\ \sf y = 50 - x \end{cases} \end{gathered}

{

4

4

x

=

4

152

y=50−x

\begin{gathered} \begin{cases} \sf x = 38 \\ \sf y = 50 - x \end{cases} \begin{array}{l}\red{(eq.1)} \\ \red{(eq.2)} \end{array}\end{gathered}

{

x=38

y=50−x

(eq.1)

(eq.2)

» Since the value of (x) is 38, there will be 38 five peso coins collected. Now identify how many one peso coins that were collected by substituting (x) to equation 2.

\begin{gathered} \begin{cases} \sf x = 38 \\ \sf y = 50 - 38 \end{cases}\end{gathered}

{

x=38

y=50−38

\begin{gathered} \begin{cases} \sf x = 38 \\ \sf y = 12 \end{cases}\end{gathered}

{

x=38

y=12

» And there you have it:

\begin{gathered} \boxed{ \sf Final \: Answer: \begin{cases}\purple{ \sf 5 \: peso \: coins \: (x)=38} \\ \purple{ \sf 1 \: peso \: coins \: (y)=12} \end{cases}}\end{gathered}

FinalAnswer:{

5pesocoins(x)=38

1pesocoins(y)=12

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