Respuesta :
Answer: 9
Step-by-step explanation:
\underline{\text{Define Variables:}}
Define Variables:
​
May choose any letters.
\text{Let }d=
Let d=
\,\,\text{the number of dimes}
the number of dimes
\text{Let }q=
Let q=
\,\,\text{the number of quarters}
the number of quarters
\text{\textquotedblleft a minimum of 18 coins"}\rightarrow \text{18 or more coins}
“a minimum of 18 coins"→18 or more coins
Use a \ge≥ symbol
Therefore the total number of coins, d+qd+q, must be greater than or equal to 18:18:
d+q\ge 18
d+q≥18
\text{\textquotedblleft at most \$3.60"}\rightarrow \text{\$3.60 or less}
“at most $3.60"→$3.60 or less
Use a \le≤ symbol
One dime is worth $0.10, so dd dimes are worth 0.10d.0.10d. One quarter is worth $0.25, so qq quarters are worth 0.25q.0.25q. The total 0.10d+0.25q0.10d+0.25q must be less than or equal to \$3.60:$3.60:
0.10d+0.25q\le 3.60
0.10d+0.25q≤3.60
\text{Plug in }\color{green}{12}\text{ for }d\text{ and solve each inequality:}
Plug in 12 for d and solve each inequality:
Elijah has 12 dimes
\begin{aligned}d+q\ge 18\hspace{10px}\text{and}\hspace{10px}&0.10d+0.25q\le 3.60 \\ \color{green}{12}+q\ge 18\hspace{10px}\text{and}\hspace{10px}&0.10\left(\color{green}{12}\right)+0.25q\le 3.60 \\ q\ge 6\hspace{10px}\text{and}\hspace{10px}&1.20+0.25q\le 3.60 \\ \hspace{10px}&0.25q\le 2.40 \\ \hspace{10px}&q\le 9.60 \\ \end{aligned}
d+q≥18and
12+q≥18and
q≥6and
​
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0.10d+0.25q≤3.60
0.10(12)+0.25q≤3.60
1.20+0.25q≤3.60
0.25q≤2.40
q≤9.60
​
\text{The values of }q\text{ that make BOTH inequalities true are:}
The values of q that make BOTH inequalities true are:
\{6,\ 7,\ 8,\ 9\}
{6, 7, 8, 9}
Therefore the maximum number of quarters that Elijah could have is 9.
