John has 4 more nickels than dimes in his pocket. Write an equation that represents, y, the value of the money John has, in terms of x, the number of dimes John has. Explain what the y–intercept of this equation represents.
Let x be the number of dimes John has. Since John has 4 more nickels than dimes, the number of nickels he has is x + 4.
The value of x dimes is 10x cents, and the value of (x + 4) nickels is 5(x + 4) cents. Therefore, the total value y of the money John has is given by:
y = 10x + 5(x + 4) = 10x + 5x + 20 = 15x + 20
So, the equation representing the value of the money John has in terms of the number of dimes is y = 15x + 20.
The y-intercept of this equation represents the value of the money John has when he has 0 dimes, which means x = 0. Plugging x = 0 into the equation, we get:
y = 15(0) + 20 = 20
Therefore, the y-intercept of the equation y = 15x + 20 represents the value of the money John has when he has no dimes, which is 20 cents.