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3 years ago

PLEASE ANSWER ALL I WILL RATE 5 STARS MARK BRAINLIEST AND THANK YOU

Mathematics

1 answer:

zepelin [54]3 years ago

8 0

Answer:

See below.

Step-by-step explanation:

13. D

Simply subtract. 85376 - 37793 = 47583.

14. C

[Something] - 32497 = 26348

Add 32497 to both sides:

[Something] - 32497 + 32497 = 26438 + 32497

[Something] = 58845

15. C

Compute each difference:

A: 51455 - 26478 = 24977

B: 49351 - 15274 = 34077

C: 63286 - 37439 = 25847

(D: 46307 - 21550 = 24757)

16. B

Simply subtract:

143864 - 112955 = 30909

17. A

First, find the difference:

85732 - 39864 = 45868

Only 45798 (A) is less than 45868.

(Note that B is equal to, not less than).

18. C

Subtract:

45932 - 29574 = 16358.

19. B

Subtract:

96834 - 31727 = 65107 - 12156 = 52951

20. C

27301 - 12352 - [Something] = 7356

14949 - [Something] = 7356

Add [Something] to each side:

14949 = 7356 + [Something]

Subtract 7356 from each side.

7593 = [Something]

Note: Do you need help with subtraction specifically? These questions can be solved with simply with a calculator, but perhaps that is not the intention here. Anyways, I recommend using Khan Academy to improve your arithmetic skills if necesary.

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A cash box contains $74 made up of quarters, half-dollars, and one-dollar

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Answer:

25 one-dollar coins, 16 half-dollar coins, and 164 quarters

Step-by-step explanation:

First, set up equations based on the information given:

$0.25q+0.50h+1.00d=74$

$\displaystyle{h=\frac{3}{5}d+1}$

$q=4(d+h)$

Then, substitute q in the first equation with the expression from the third equation:

$0.25[4(d+h)]+0.50h+1.00d=74\\1d+1h+0.50h+1.00d=74\\2d+1.5h=74$

Next, substitute h in that equation with the expression from the second equation:

$\displaystyle{2d+1.5(\frac{3}{5}d+1)=74}$

$2d+0.9d+1.5=74\\2.9d+1.5=74$

Solve for d, the number of one-dollar coins:

$2.9d+1.5=74\\2.9d=72.5\\d=25$

Substitute 25 for d in the second equation to find h, the number of half-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{h=\frac{3}{5}(25)+1}$

$h=15+1\\h=16$

Substitute 25 for d and 16 for h in the third equation to find q, the number of quarters:

$q=4(d+h)\\q=4(25+16)\\q=4(41)\\q=164$

Then, verify that the coins total $74:

$0.25(164)+0.50(16)+1.00(25)=74\\41+8+25=74\\74=74\\\text{Check.}$

Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{16=\frac{3}{5}(25)+1}$

$16 = 15 + 1\\16 = 16\\\text{Check.}$

Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:

$q=4(d+h)\\164=4(25+16)\\164=4(41)\\164=164\\\text{Check.}$

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3 years ago