Question

1. bellamy has dimes, nickels, and pennies in his pocket. he has two more nickels than dimes, and three times as many pennies as nickels. how many pennies does he have if he has $0.52 in his pocket?

Explanation:

Step1: Define variables for coins

Let $d$ = number of dimes, $n$ = number of nickels, $p$ = number of pennies.

Step2: Set up relation equations

$n = d + 2$ (2 more nickels than dimes)
$p = 3n = 3(d + 2)$ (3x pennies as nickels)

Step3: Convert total value to cents

Total value = 52 cents (since $\$0.52 = 52$ cents)

Step4: Write value equation

$10d + 5n + 1p = 52$

Step5: Substitute $n$ and $p$

$10d + 5(d+2) + 3(d+2) = 52$

Step6: Expand and simplify

$10d + 5d + 10 + 3d + 6 = 52$
$18d + 16 = 52$

Step7: Solve for $d$

$18d = 52 - 16 = 36$
$d = \frac{36}{18} = 2$

Step8: Calculate number of pennies

$p = 3(d+2) = 3(2+2) = 3\times4 = 12$

Answer:

12