Answer:
The number of nickles is 6
The number of dims is 12 .
Step-by-step explanation:
Given as :
Sum of total number of dims and nickels coins = 18
The value of total combination = $1.50
Let The total number of dims = d
Let The total number of nickels = n
1 nickles = $0.05
1 dims = $0.1
According to question
Total number of dims and nickels coins = number of dims + number of nickels
Or, d + n = 18 .........1
And
$0.1 ×d + $0.05 ×n = $1.50
Or, 0.1 d + 0.05 n = 1.50 .........2
Now, Solving eq 1 an eq 2
0.1 × (d + n) - (0.1 d + 0.05 n) = 0.1 × 18 - 1.50
Or, (0.1 d - 0.1 d) + (0.1 n - 0.05 n) = 1.8 - 1.50
Or, 0 + 0.05 n = 0.3
Or, 0.05 n = 0.3
∴ n = [tex]\dfrac{0.3}{0.05}[/tex]
i.e n = 6
So, The number of nickles = n = 6
Put the value of n int eq 1
∵ d + n = 18
Or, d = 18 - n
Or, d = 18 - 6
i.e d = 12
So, The number of dims = d = 12
Hence, The number of nickles is 6 and the number of dims is 12 . Answer
Answer:
Since the point (2,12) is inside the double shaded region, one possible solution to the system of inequalities would be:
Sarah could have 2 nickels and 12 dimes.
Step-by-step explanation:
Variable Definitions:
x = the number of nickels
y = the number of dimes
“a maximum of 18 coins" → 18 or fewer coins
Therefore the total number of coins, x + y, must be less than or equal to 18:
x + y ≤ 18
“no less than $1.20" → $1.20 or more
One nickel is worth $0.05, so x nickels are worth 0.05x. One dime is worth $0.10, so y dimes are worth 0.10y. The total 0.05x+0.10y must be greater than or equal to $1.20:
0.05x + 0.10y ≥ 1.20
Solve each inequality for y:
x + y ≤ 18 0.05x + 0.10y ≥ 1.20
y ≤ 18−x 0.10y ≥ 1.20 − 0.05x
y ≥ 1.20 - 0.05x / 0.10
y ≥ 12 − 1/2x
Graph y ≤ 18 − x by shading down and graph y ≥ 12 − 1/2x by shading up: (png given)
