what should happen?

Question

A child’s bank contains $6.30 in dimes and quarters. There are twice as many dimes as quarters. How many of each kind of coin are in the bank?

a 24 dimes and 12 quarters

b 26 dimes and 13 quarters

c 28 dimes and 14 quarters

d No solution, not enough information.



The average of four consecutive even integers is 17. Find the integers.

a 15, 16, 17, and 18

b 16, 18, 20, and 22

c 14, 16, 18, and 20

d No solution, contradictory facts

Answer 1

q = # of quarters
d = # of dimes

There are twice as many dimes as quarters

1) d = 2q

bank contains $6.30 in dimes and quarters.

2) 10d + 25q = 630 {pennies}

Substitute fro d from equation 1

10(2q) + 25q = 630
20q + 25q = 630
45q = 630
q = 14

d = 2(14) = 28


The average of four consecutive even integers is 17. Find the integers

[n + (n + 2) + (n + 4) + (n + 6)]/4 = 17

[4n + 12]/4 = 17

n + 3 = 17

n = 14

check

(14 + 16 + 18 + 20)/4 = 17

68/4 = 17

17 = 17

Answer 2

Child's bank contents:
Let x = no. of quarters, 2x = number of dimes

Finding no. of quarters:
$0.25x + $0.10(2x) = $6.30
$0.25x + $0.20x = $6.30
$0.45x = $6.30
x = 14

Finding no. of dimes:
= 14 * 2
= 28

Answer: c which indicates 14 quarters and 28 dimes

Four consecutive number:
x = 1st, x + 2 = 2nd, x + 4 = third, x + 6 = 4th

Finding the first number:
(x + x + 2 + x + 4 + x + 6) / 4 = 17
4x + 12 = 68
4x = 56
x = 14

2nd, 3rd, 4th numbers, respectively::
16 (14 + 2), 18 (14 + 4), 20(14 + 6)

Proof (average of the numbers is 17):
= (14 + 16 + 18 + 20)/4
= 68/4
= 17

Answer 3

c.
28x10=2.80
14x25=3.50
2.80+3.50=6.30

c.
14+16+18+20=68
68/4=17

Answer 4

What should happen? you should already know this is what should happen just use variables to solve for nickels and dimes, for the second problem the answers not a nor b nor d. come on now. use logic.

Answer 5

What does the question "what should happen?" have to do with this or any other math problem?