help with math problem

Question

David’s coin collection is valued at $22.70. He has one fewer half-dollar coin than twice the number of dimes and four more quarters than three times the number of dimes. How many dimes, quarters, and half-dollars does David have, assuming he has no other coins

Answer 1

D = number of dimes

H = number of half dollars

Q = number of quarters

one fewer half-dollar coin than twice the number of dimes

H = 2D - 1

four more quarters than three times the number of dimes

3D + 4 = Q

The equation you want to solve is

50H + 25Q. + 10D = 2270

50H because each half dollar is worth 50 cents

25Q because each quarter is worth 25 cents

10D because each dime is worth 10 cents

Find out the number of dimes by using

2D - 1 for H

and

3D + 4 for Q

50H + 25Q + 10D

50(2D - 1) + 25(3D + 4) + 10D. =. 2270

50(2D) - 50(1) + 25(3D) + 25(4) + 10D = 2270

100D - 50 + 75D + 100 + 10D = 2270

+ 50 = 50

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100D +. 75D + 100 + 10D = 2320

-100. = -100

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100D + 75D + 10D = 2220

185D = 2220 Now you want to get D alone, so divide each side by 185

185D/185 = 2220/185

D = 2220/185

D = 12

2D - 1 = H

2(12) - 1 = H

24 - 1 = H

23 = H

3D + 4 = Q

3(12) + 4 = Q

36 + 4 = Q

40 = Q

NOW CHECK TO SEE IF YOU ARE CORRECT

23 = H, there are 23 half dollars

40 = Q, there are 40 quarters

12 = D, there are 12 dimes

50H + 25Q + 10D = 2270

50(23) + 25(40) + 10(12) = 2270

1150 + 1000 + 120 = 2270

Answer 2

Jorge,

The is a problem of finding 3 unknowns. Let d represent the number of dimes, q represent the number of quarters, and h represent the number of half-dollars. We need at least 3 different relationships (equations) to solve for the 3 unknowns.

The total value (in dollars) of the dimes is 0.10•d; for the quarters it's 0.25•q; and for the half-dollars is 0.50•h.

From the first sentence, we know the total amount, so we can write

0.10•d + 0.25•q + 0.50•h = 22.70

From the second sentence, we can write 2 more equations:

h = 2•d - 1 and q = 3•d + 4

That's all the conceptual stuff. The rest is substitution and simplification arithmetic. First, rewrite the first equation in terms of d only, by substitution:

0.10•d + 0.25•(3•d + 4) + 0.50•(2•d - 1) = 22.70

Distribute:

0.10•d + 0.75•d + 1.00 + 1.00•d - 0.50 = 22.70

Consolidating:

1.85•d + 0.50 = 22.70

Subtracting 0.5 from both sides:

1.85•d = 22.20

Dividing both sides by 1.85 results in d = 12. Now, we know there are 12 dimes.

Plugging this value into the 2nd and 3rd equations:

h = 2•d - 1 = 2•12 - 1 = 23

q = 3•d + 4 = 3•12 + 4 = 40

In addition to the 12 dimes, there are 23 half-dollars and 40 quarters. As a check, it is good practice to substitute these values into the first equation to verify that it comes to $22.70.

Answer 3

D = number of dimes

2D - 1 = number of half dollars

3D + 4 = number of quarters

value of dimes = 0.10*D

value of half dollars = 0.50 * (2D - 1)

value of quarters = 0.25 * (3D+4)

total value = 22.70

0.10D + 0.50*(2D-1) + 0.25*(3D+4) = 22.70

0.10D + D - 0.50 + 0.75D + 1.00 = 22.70

1.85D + 0.50 = 22.70

1.85D = 22.20

D = 12

Half dollars = 2D-1 = 23

Quarters = 3D + 4 = 3*12+4 = 40

Answer 4

(2d-1).5+(3d+4).25=22.7

d-.5 +.75d+1 = "

1.75d+.5=22.7

1.75d=22.2

d=12.6857...........

This is the best I can do.