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Nora's paper airplane flew 9 1/6 feet. That was 2 3/4 feet farther than Max's plane flew. Write and solve an equation to show ho

stepan [7]

Answer:

Max's paper airplane flew $\frac{77}{12}$ feet or $6\frac{5}{12}$ feet.

Step-by-step explanation:

As Nora's paper airplane flew 9 1/6 feet

i.e.

$9\frac{1}{6}=\frac{55}{6}$

Nora's paper was farther than Max's plane flew by = 2 3/4 feet

i.e.

$2\frac{3}{4}=\frac{11}{4}$

Thus the equation to show how far Max's paper airplane flew is:

$\:\:9\frac{1}{6}-2\frac{3}{4}$

$=\frac{55}{6}-\frac{11}{4}$

$\mathrm{Least\:Common\:Multiplier\:of\:}6,\:4:\quad 12$

$\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}$

$=\frac{110}{12}-\frac{33}{12}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$=\frac{110-33}{12}$

$\mathrm{Subtract\:the\:numbers:}\:110-33=77$

$=\frac{77}{12}$

$=6\frac{5}{12}$

Therefore, Max's paper airplane flew $\frac{77}{12}$ feet or $6\frac{5}{12}$ feet.

6 0

3 years ago

A jeweler wants to make 14 grams of an alloy that is precisely 75% gold.. The jeweler has alloys that are 25% gold, 50% gold, &a

Goryan [66]

Given that the jeweler has alloys that are 25% gold, 50% gold, and 82% gold.

As he wants to make 14 grams of an alloy by adding two different alloys that is precisely 75% gold, so one alloy must have a percentage of gold more than 75%.

One alloy is 82% gold and, the second can be chosen between 25% gold, 50% gold, so there are two cases.

Case 1: 82% gold + 50% gold

Let x grams of 82% gold and y grams of 50% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 50% of y

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times y \\\\$

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times (14-x)$ [as x+y=14]

$\Rightarrow 75 \times 14 = 82 \times x + 50 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 50 \times14-50\times x \\\\\Rightarrow 75 \times 14 = 32 \times x + 50 \times14 \\\\\Rightarrow 32 \times x =75 \times 14 - 50 \times14 \\\\$

$\Rightarrow x =(25 \times 14)/32=10.9375$ grams

and $y = 14-x= 14-10.9375=3.0625$ grams.

Hence, 10.9375 grams of 82% gold and 3.0625 grams of 50% gold added to make 14 grams of 75% gold.

Case 2: 82% gold + 25% gold

Let x grams of 82% gold and y grams of 25% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 25% of y

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times y \\\\\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times (14-x) \\\\ \Rightarrow 75 \times 14 = 82 \times x + 25 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 25 \times14-25\times x \\\\\Rightarrow 75 \times 14 = 57 \times x + 25 \times14 \\\\\Rightarrow 57 \times x =75 \times 14 - 25 \times14 \\\\$

$\Rightarrow x =(50 \times 14)/57=12.28$ grams

and $y = 14-x= 14-12.28=1.72$ grams.

Hence, 12.28 grams of 82% gold and 1.72 grams of 50% gold added to make 14 grams of 75% gold.

3 0

3 years ago

Item 15 Solve the equation for y. 20=5x+10y

Ronch [10]

Answer:

Rewrite the equation as

5

x

+

10

y

=

20

5

x

+

10

y

=

20

.

5

x

+

10

y

=

20

5

x

+

10

y

=

20

Subtract

5

x

5

x

from both sides of the equation.

10

y

=

20

−

5

x

10

y

=

20

-

5

x

Divide each term by

10

and simplify.

y=2−x/ 2

Step-by-step explanation:

5 0

3 years ago

I need help !!!!!!!!!!!

Anna71 [15]

I cant see the picture

4 0

3 years ago

Read 2 more answers

Evaluate each expression.

Sindrei [870]

Answer:

gghifghdfighdfghdfiuhofudk

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

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I'm stuck with this question