All categories

3 years ago

What is the solution to the system of equations 1/4x+1 1/2y=5/8 3/4x-1 1/2y=3 3/8

Mathematics

1 answer:

AleksandrR [38]3 years ago

6 0

Answer:

$\large\boxed{x=4,\ y=-\dfrac{1}{4}}$

Step-by-step explanation:

$\underline{+\left\{\begin{array}{ccc}\dfrac{1}{4}x+1\dfrac{1}{2}y=\dfrac{5}{8}\\\\\dfrac{3}{4}x-1\dfrac{1}{2}y=3\dfrac{3}{8}\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\dfrac{4}{4}x=3\dfrac{8}{8}\\\\.\qquad\boxed{x=4}\\\\\text{put the value of x to the first equation:}\\\\\dfrac{1}{4}(4)+1\dfrac{1}{2}y=\dfrac{5}{8}\\\\1+1\dfrac{1}{2}y=\dfrac{5}{8}\qquad\text{subtract}\ 1=\dfrac{8}{8}\ \text{from obth sides}\\\\1\dfrac{1}{2}y=-\dfrac{3}{8}\qquad\text{multiply both sides by 2}\\\\3y=-\dfrac{3}{4}\qquad\text{divide both sides by 3}\\\\\boxed{y=-\dfrac{1}{4}}$

You might be interested in

4g + 3(-3 + 4g) = 1-g. Solve the equation. Can someone help me ASAP. I'm confused

Olegator [25]

4g+3(-3+4g)=1-g
Distribute the 3(-3+4g)
4g-9+12g=1-g
Add 4g and 12g
16g-9=1-1g
Add 1g and 16g (variables always have an invisible 1 in front)
17g-9=1
Add 9 and 1
17g=10
Divide both sides by 17 and the answer is g=10/17

5 0

3 years ago

Judy is making scarves to give to her family as gifts. She needs to make 5 scarves and each scarf is 3.75 feet long. How many ya

Trava [24]

You multiply five by 3.75 and you get 18.75 ft. to get yards you divide by three and you get 6.25 yards

6 0

3 years ago

Help. Solving Multi Step Ratio Problems!

Romashka-Z-Leto [24]

Answer:

Part 1) $30\ coupons$

Part 2) $12\ sandwiches$

Part 3) $60\ push-ups$

Part 4) $96\ minutes$

Part 5) $\$95$

Part 6) $1\frac{7}{8}\ cups\ of\ pretzel$

Step-by-step explanation:

Part 1) we know that

At the Green House of Salad , you get a $1 coupon for every 3 salads you buy

Using proportion

Find out the number of salads you could buy to get $10 in coupons

$\frac{1}{3}=\frac{10}{x} \\\\x=3(10)\\\\x=30\ coupons$

Part 2) we know that

Kim orders catering for $35

She spend $5 on a large order of potato salad and the rest on turkey sandwiches

Each sandwich is $2.50

How many sandwiches does Kim buy?

step 1

Find out how many Kim spent on turkey sandwiches

Subtract $5 from $35

35-5=$30

step 2

Using proportion, find out the number of sandwiches

$\frac{1}{2.50}=\frac{x}{30}\\\\x=30/2.50\\\\x= 12\ sandwiches$

Part 3) we know that

Molly does 10 push-ups at the same time as Liza does 15 push-ups

Using proportion

Find out how many push-ups Liza does when Molly does 40 push-ups

$\frac{10}{15}=\frac{40}{x}\\\\x=15(40)/10\\\\x=60\ push-ups$

Part 4) we know that

A shark swim at a speed of 25 miles per hour

The shark rest after 40 miles

How long in minutes, does the shark swim before resting?

Using proportion

Find out how long in minutes the shark swim 40 miles

Remember that

$1\ h=60\ min$

$\frac{25}{60}\ \frac{miles}{minutes}=\frac{40}{x}\ \frac{miles}{minutes}\\\\x=60(40)/25\\\\x=96\ minutes$

Part 5) we know that

For every bar of soap that Aly sells, she earns $5

For every mug that Janet sells, she earns twice as much as Aly

Aly sells 5 bars of soap and Janet sells 7 mugs

How much money did they make altogether?

step 1

Find out the amount earned by Aly

using proportion

$\frac{1}{5}=\frac{5}{x}\\\\x=5(5)\\\\x=\$25$

step 2

Find out the amount earned by Janet

Remember that

For every mug that Janet sells, she earns twice as much as Aly

For every mug that Janet sells, she earns 2($5)=$10

using proportion

$\frac{1}{10}=\frac{7}{x}\\\\x=10(7)\\\\x=\$70$

step 3

Adds the amount earned by Aly plus the amount earned by Janet

$25+70=\$95$

Part 6) we know that

Ted is making trail mix for a party

He mixes 1 1/2 cups of nuts, 1/4 cup of rising and 1/4 cup of pretzel

How many cups of pretzel does Ted need to make 15 cups of trail mix?

Adds the quantities

$1\frac{1}{2}+\frac{1}{4} +\frac{1}{4}=2\ cups\ of \ trail\ mix$

That means

For every 2 cups of trail mix we need 1/4 cup of pretzel

using proportion

Find out how many cups of pretzel does Ted need to make 15 cups of trail mix

$\frac{2}{(1/4)}=\frac{15}{x}\\\\x=15(1/4)/2\\\\x=\frac{15}{8}\ cups\ of\ pretzel$

Convert to mixed number

$\frac{15}{8}=\frac{8}{8}+\frac{7}{8}=1\frac{7}{8}\ cups\ of\ pretzel$

6 0

3 years ago

Find last year's salary if, after a 5 %5% pay raise, this year's salary is $ 33 comma 075$33,075.

Anvisha [2.4K]

$33,075 = 0.05S + S

$33,075 = 1.05S

$33,075/1.05 = 1.05S/1.05

S= $31,500

Check

$31,500 * 5% = $1575 + $31,500 =$33,075

8 0

3 years ago

What is the net force on the image(NEED ASAP)

ollegr [7]

Answer:

1200 N right

Step-by-step explanation:

Subtract 150 from 1350. Since there is more force towards the right, the net force is 1200 N right

8 0

2 years ago

Read 2 more answers