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8090 [49]
3 years ago
14

Divide $500 in these ratios using the unitary method. A. 2:3 B. 3:7 C. 1:1

Mathematics
1 answer:
zysi [14]3 years ago
3 0

Answer:

A) 200 is to 300 dollars

B)150 is to 350 dollars

C) 250 is to 250

Step-by-step explanation:

Part A) We want to divide $500 in the ratio 2:3 using the unitary method.

The total ratio is 2+3=5.

This means one unit is \frac{500}{5}=$100

Therefore $500 in the ratio 2:3 is 2*100=200 to 3*100=300

Part B) We want to divide $500 in the ratio 3:7 using the unitary method.

The total ratio is 3+7=10.

This means one unit is \frac{500}{10}=$50

Therefore $500 in the ratio 3:7 is 3*50=150 to 7*50=350

Part C) We want to divide $500 in the ratio 1:1 using the unitary method.

The total ratio is 1+1=2.

This means one unit is \frac{500}{2}=$250

Therefore $500 in the ratio 1:1 is 1*250=250 to 1*250=250

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Please help this is past due
Rom4ik [11]

Answer:

See below.

Step-by-step explanation:

Alexi originally has $43 in his bank account and deposits $7 per week.

Week 1: $50

Week 2: $57

Week 3: $64

Week 4: $71

Week 5: $78

The pattern is that it increased $7 every week starting from $43.

A pattern rule would be: y = 7x + 43 where x represents the number of weeks.

7 0
3 years ago
(Hehe...Please ignore the markings)
inysia [295]

Answer:

See below:

Step-by-step explanation:

Problem 1:

Multiply Equation 1 by 4, keep Equation 2 the same.

x+y=8, multiply each term by 4:

4*x=4x, 4*y=4y, 8*4=32

so, the equivalent system is: 4x+4y=32 and x-y=2

Solve the system of equations:

x-y=2 becomes x=y+2

plug into 4x+4y=32 to solve for y

4(y+2)+4y=32---> 4y+8+4y=32--->8y=24---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 1 Answer:

Equivalent system: 4x+4y=32, x-y=2; solution: x=5, y=3

Problem 2:

Keep Equation 1 the same. Add 1 and 2.

To add an equation, add the left sides together, and then the rights.

so: x+y=8 + x-y=2 gives us: 2x=10

solve for x ---> 2x/2=10/2--->x=5

plug x into x+y=8--->5+y=8--->y=3

Problem 2 answer:

Equivalent system: x+y=8, 2x=10; solution:x=5, y=3

Problem 3:

Subtract Equation 2 from 1, and keep 2 the same.

To subtract an equation, subtract the left sides, then the rights. We are subtracting 1<em> from </em>2, so its 2-1.

x-y=2 - x+y=8 gives us: -2y=-6

Solve for y by dividing by -2-->-2y/-2=-6/-2---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 3 answer:

Equivalent system: -2y=-6, x-y=2; solution: x=5, y=3

Problem 4:

Multiply the sum of Equation 1 and 2 by a factor of 3. Keep equation 2 the same.

First we add 1 and 2: (we did this earlier) ---> 2x=10 ---> now we multiply it all by 3---> 2x*(3)=10*(3)---> this gives us: 6x=30---> now divide by 6 to solve for x: 6x/6=30/6 gives us: x=5

Now, solve for y by plugging x into equation 2: x-y=2---> 5-y=2--->y=3

Problem 4 answer:

Equivalent system: 6x=30, x-y=2; solution: x=5, y=3

______

Quick Tip: One thing inherent of Equivalent systems is that they have the same set of solutions. Thus, we know the systems are equivalent when they have the same set of solutions for x and y. Moreover, you don't need to solve every time after you attempt to find an equivalent system, instead, just plug in the values found in problem 1 to each new set of equations to test if they are equivalent.

If we find x=5 and y=3 for x+y=8 and x-y=2, then all we have to do is plug them in to 6x=30 and -2y=-6 to see if they are equivalent.

6(5)=30 ---> true

-2(3)=-6 ---> true

3 0
3 years ago
2y to the power of 2x - 3xz = ?
MrRissso [65]

Answer:

x•(2xy-3z)

Step-by-step explanation:

2x²y -3xz== x(2xy-3z)

6 0
3 years ago
Joe went on holiday to Spain.
Hunter-Best [27]
Answers:

a. £2,090
b. My answer would be less because my total in euros would be divided by a greater number when converting euros to pounds.

Work for part a:

Apartment: 560•3= 1680 euros

Car: 20.16•15= 302.4 euros

1680+302.4=1982.4

1982.4/1.12 = £x/1

1982.4 / 1.12= £1,770

£1,770 + £320 = £2,090 total

Work for part b:
Example:
(instead of 1.12 I put 2 to see what would happen with a greater number)
1982.4 / 2 = 991.2

991.2 is less than 1,770 (the answer I got with 1.12)

Let me know if you need any clarification! :)
7 0
3 years ago
I need help I don't understand it at all
DedPeter [7]

Answer:

x = 9

Step-by-step explanation:

Given

5x - 31 = 23 - x ( add x to both sides )

6x - 31 = 23 ( add 31 to both sides )

6x = 54 ( divide both sides by 6 )

x = 9

8 0
3 years ago
Read 2 more answers
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