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TRANSLATING DESCRIPTIONS INTO ALGEBRAIC EXPRESSIONS

Meanings of Mathematical Words and Phrases

\begin{tabular}{|c|c|}
\hline
Verbal Representation & Algebraic Representation or Example \\
\hline
a number, some number & variables like [tex]$x, y, z, a, b$[/tex], or [tex]$c$[/tex] \\
\hline
length of, more than, greater than &
\begin{tabular}{l}
[tex]$3+a \leftrightarrow$[/tex] "the sum of 3 and a number" \\
(3 is a constant and [tex]$a$[/tex] is a variable in this expression)
\end{tabular} \\
\hline
of, less than &
\begin{tabular}{l}
[tex]$5-y \leftrightarrow$[/tex] "a number less than 5" \\
(5 is a constant and [tex]$y$[/tex] is a variable in this expression)
\end{tabular} \\
\hline
product of &
\begin{tabular}{l}
[tex]$12r \leftrightarrow$[/tex] "the product of 12 and a number" \\
(12 is a coefficient and [tex]$r$[/tex] is a variable in this expression)
\end{tabular} \\
\hline
quotient of, ___ by &
\begin{tabular}{l}
[tex]$\frac{q}{7} \leftrightarrow$[/tex] "the quotient of a number and 7" \\
([tex]$q$[/tex] is a variable and [tex]$7$[/tex] is a constant in this expression)
\end{tabular} \\
\hline
the quantity of &
\begin{tabular}{l}
grouping symbols like parentheses, as in \\
[tex]$4(a+2) \leftrightarrow$[/tex] "4 times the quantity of [tex]$a$[/tex] plus 2" \\
(4 is a constant and [tex]$a$[/tex] is a variable in this expression)
\end{tabular} \\
\hline
power of, raised to &
\begin{tabular}{l}
an exponent, as in \\
[tex]$7^n \leftrightarrow$[/tex] "7 raised to a number" \\
([tex]$7$[/tex] is a base and [tex]$n$[/tex] is an exponent in this expression)
\end{tabular} \\
\hline
\end{tabular}

Guided Notes: Expressions



Answer :

GinnyAnswer
Let's break down the problem step-by-step:

Manuel collects coins. He already has 523 coins and he earns 42 coins each week. How many coins will he have after 15 weeks?

1. Identify the initial number of coins:
Manuel already has 523 coins. Let's denote this as [tex]\( C_0 = 523 \)[/tex], where [tex]\( C_0 \)[/tex] is the initial number of coins.

2. Determine the number of coins earned per week:
Manuel earns 42 coins each week. We can denote this as [tex]\( E = 42 \)[/tex], where [tex]\( E \)[/tex] is the earnings per week.

3. Identify the number of weeks:
We are given the number of weeks as 15. We'll denote this as [tex]\( W = 15 \)[/tex], where [tex]\( W \)[/tex] represents the number of weeks.

4. Calculate the total number of coins earned over 15 weeks:
To find out how many coins Manuel earns in 15 weeks, we multiply the number of weeks by the coins earned per week.

[tex]\[ \text{Total coins earned in 15 weeks} = E \times W = 42 \times 15 \][/tex]

According to the provided answer, the total number of coins earned over 15 weeks is 630 coins. Symbolically, this is:

[tex]\[ E \times W = 630 \][/tex]

5. Calculate the total number of coins after 15 weeks by adding the initial number of coins:
Now, we add the initial number of coins to the total coins earned in 15 weeks to find the final number of coins:

[tex]\[ \text{Total coins after 15 weeks} = C_0 + (E \times W) = 523 + 630 \][/tex]

According to the provided answer, the total number of coins after 15 weeks is 1153 coins. Symbolically, this is:

[tex]\[ 523 + 630 = 1153 \][/tex]

So, Manuel will have a total of 1153 coins after 15 weeks.

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