Question

13. COINS Declan has 17 coins in his pocket. All the coins are dimes and quarters. The value of the coins is 290 cents. Define variables and write a system of equations to find the number of dimes and quarters Declan has. Then solve the system graphically.​

Answer 1

Declan has 9 dimes and 8 quarters in his pocket.

Equation

An equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the number of dimes and y represent the number of quarters.

A dime is worth 10 cents. A quarter is worth 25 cents.

Hence:

x + y = 17    (1)

Also:

10x + 25y = 290  (2)

From equation 1 and 2:

x = 9, y = 8

Declan has 9 dimes and 8 quarters in his pocket.

Find out more on equation at: brainly.com/question/22688504

Answer 2

Answer:

• 9 dimes
• 8 quarters

Step-by-step explanation:

The problem requests numbers of dimes and quarters, so we can assign a variable to each of those numbers. Let x and y represent the numbers of dimes and quarters Declan has, respectively. (If we were solving this by hand, we might choose d and q to remind us what they stand for. Solving graphically, we use variables the graphing calculator recognizes.)

The problem statement tells us two relationships between these variables:

  x + y = 17 . . . . . the total number of coins is 17

  10x +25y = 290 . . . . .  the total value of the coins is 290 cents

(Note that a dime is worth 10 cents, so the number of cents represented by x dimes is 10x cents.)

__

The attached graph shows the solution to these equations. It is the point where the lines cross: (x, y) = (9, 8).

Declan has 9 dimes and 8 quarters.

_____

Additional comment

We prefer a graphing calculator for finding graphical solutions.

If you're doing this by hand, you can graph the equations using their x- and y-intercepts. Each of those is found by solving the equation when the other variable is zero.

These equations are in "standard form:"

  ax +by = c

Then the intercepts are ...

  x-intercept = c/a

  y-intercept = c/b

__

The y-intercept corresponding to the number of quarters is not on an integer point. (It is y = 290/25 = 11.6.) To plot the line for the second equation, you may want to choose y=10, so x=4. The point (4, 10) will be on that line, making the line easier to plot.