Answer:
Step-by-step explanation:
A dime is worth 10 cents. Converting to dollars, it becomes 10/100 = $0.1
A quarter is worth 25 cents. Converting to dollars, it becomes 25/100 = $0.25
Let x represent the number of dimes that Jayden has.
Let y represent the number of quarters that Jayden has.
Jayden has some dimes and some quarters. He has at most 25 coins. It means that
x + y ≤ 25
The coins worth at least $4.60 combined. It means that
0.1x + 0.25y ≥ 4.6 - - - - - - - - - - 1
If Jayden has 7 dimes, then
7 + y ≤ 25
y ≤ 25 - 7
y ≤ 18
Substituting x = 7 into equation 1, it becomes
0.1 × 7 + 0.25y ≥ 4.6
0.7 + 0.25y ≥ 4.6
0.25y ≥ 4.6 - 0.7
0.25y ≥ 3.9
y ≥ 3.9/0.25
y ≥ 15.6
All possible values for the number of quarters that he could have would be
15.6 ≤ y ≤ 18
Answer:
16,17,18
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 at most 25 coins"}\rightarrow \text{25 or fewer coins}
“at most 25 coins"→25 or fewer coins
Use a \le≤ symbol
Therefore the total number of coins, d+qd+q, must be less than or equal to 25:25:
d+q\le 25
d+q≤25
\text{\textquotedblleft at least \$4.60"}\rightarrow \text{\$4.60 or more}
“at least $4.60"→$4.60 or more
Use a \ge≥ 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 greater than or equal to \$4.60:$4.60:
0.10d+0.25q\ge 4.60
0.10d+0.25q≥4.60
\text{Plug in }\color{green}{7}\text{ for }d\text{ and solve each inequality:}
Plug in 7 for d and solve each inequality:
Jayden has 7 dimes
\begin{aligned}d+q\le 25\hspace{10px}\text{and}\hspace{10px}&0.10d+0.25q\ge 4.60 \\ \color{green}{7}+q\le 25\hspace{10px}\text{and}\hspace{10px}&0.10\left(\color{green}{7}\right)+0.25q\ge 4.60 \\ q\le 18\hspace{10px}\text{and}\hspace{10px}&0.70+0.25q\ge 4.60 \\ \hspace{10px}&0.25q\ge 3.90 \\ \hspace{10px}&q\ge 15.60 \\ \end{aligned}
d+q≤25and
7+q≤25and
q≤18and
0.10d+0.25q≥4.60
0.10(7)+0.25q≥4.60
0.70+0.25q≥4.60
0.25q≥3.90
q≥15.60
\text{The values of }q\text{ that make BOTH inequalities true are:}
The values of q that make BOTH inequalities true are:
\{16,\ 17,\ 18\}
{16, 17, 18}
