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3 years ago

Sasha can mow 3/8 of an acre of grass in 45 minutes. How many acres of grass does Sasha mow per hour

Mathematics

1 answer:

bekas [8.4K]3 years ago

3 0

Sasha moves 1/2 of an acre per hour

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

Strike441 [17]

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

Your aunt is asking your help in figuring out how to

Marizza181 [45]

Answer:

650

Step-by-step explanation:

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2 years ago

Ms. Jones had $40 to purchase groceries. She bought 4 packs of rice and 3 boxes of granola bars. The packs of rice cost $1.09 ea

Nesterboy [21]

Answer:

so to know full price of granola bars and rice packs; you would multiply 1.09 × 4 for the rice which you get 4.36 then for granola bars you do 4.29 × 3 and you get 12.87 then you add 12.87 + 4.36 = 17.23 then you subtract this from the $$ Mr.Jones has which is 40 so its 40-17.23 and you get 22.77

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3 years ago

Simplify the expression. 11(32 + 5x) + 4x - x

alex41 [277]

Answer:

352+58x

Step-by-step explanation:

Distribute to get 352+55x+4x-x

Combine like terms to get 352+58x.

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3 years ago

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Factor 1/6 out of 1/6x+1/6

lesya692 [45]

Answer:

1/6(1x+1)

Step-by-step explanation:

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3 years ago