1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lidiya [134]
3 years ago
9

the larger of two numbers is 7 less than three times the smaller number. if the sum of the numbers is 61, find the numbers

Mathematics
1 answer:
adoni [48]3 years ago
8 0

Let X = the large #

    Y = the small #

We have 2 unknowns, therefore we need 2 equations to solve for them:

    X + Y = 61

    X = 3Y - 7

Using the substitution method we get:

    X + Y = 61                original equation

   (3Y - 7) + Y = 61        substituting for X

    4Y - 7 = 61                combine like terms

    4Y - 7 + 7 = 61 + 7    add 7 to both sides

    4Y = 68                     simplify

    4Y/4 = 68/4               divide both sides by 4

    Y = 17                       solve for Y

    X + Y = 61                 original equation

    X + 17 = 61                replace Y with 17

    X + 17 - 17 = 61 - 17  subtract 17 from both sides

    X = 44                        solve for X

Check your answer:

       X + Y = 61          X = 3Y - 7

     44 + 17 = 61        44 = 3(17) - 7

     61 = 61  check!     44 = 51 - 7

                                 44 = 44  check!

Therefore, the larger #(X) = 44 and the smaller #(Y)= 17.

You might be interested in
A Sum of $14 is made of 92 coins consisting of dimes and quarters. How Many are there of each kind of coin
steposvetlana [31]
So first I would say, what if all of them were dimes, how far away would it be from $14?

So 92 coins * 10 cents = $9.20

So it's 4.80 dollars away from 14 dollars.

So if we were to switch one to a quarter, it would increase by 0.15 cents.

So we want to see how many increases we need to reach 4.80 dollars more.

4.80/0.15 = 32

So there are 32 quarters and 60 dimes.
7 0
3 years ago
Read 2 more answers
A menu has three meat choices,
wolverine [178]

Answer:

18 ways

Step-by-step explanation:

Number of Meat choices = 3

Number of Vegetable choices = 3

Number of Desserts = 2

Number of ways dinner can be chosen :

Number of meat choices * Number of vegetable choices * number of desserts

3 * 3 * 2

= 18

Hence, dinner can be chosen in 18 different choices.

4 0
2 years ago
If randy earns $12.74 per hour, what is his overtime rate? How much should randy make if he works 45 1/2 hours during 1 week?
elena-14-01-66 [18.8K]

Answer:

$19.24 is the overtime rate $579.67 one week

Step-by-step explanation:

So $13.00 its $19.50 so I subtracted $12.74 to $13.00 got 0.26 then subtracted $19.50 by 0.26 and got $19.24

$12.74 times 45.5 that will be $579.67 for just one week

If I didn't get it right. Tell me in the comments. I think I got it right.

8 0
3 years ago
Jessica had 207 dollars to spend on 8 books. After
Aleksandr-060686 [28]

207$ - 15$ = 192$

192$ : 8 = 24$

Answer: Each book costed 24$.

6 0
3 years ago
Find the value of b. Enter as an exact, simplified value:
Zanzabum

Answer: 3sqrt6

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • Clark is having a party at his house. His father has allowedhim to spend at most $20 on snack food. He’d like to but chips that
    14·1 answer
  • Solve rx = 30 for x.
    9·2 answers
  • - 3x + 9 - 4 = x + 3 + 2x​
    8·2 answers
  • Change 3240 degrees/second to radians/second
    8·1 answer
  • Find the value of x. (2x) and (x+15)
    5·2 answers
  • Which two problems below does this model represent? <br><br> 12 x 2<br> 24 ÷ 6<br> 6 x 4<br> 24 x 6
    12·1 answer
  • = 2 - 4
    13·1 answer
  • (Please Help! : NO LINKS)
    12·1 answer
  • The length of the sides of a triangle are in the ratio 3:5:7. The difference between the longest side and the shortest side is 2
    10·1 answer
  • Two linear functions are combined with addition, and then the same two linear functions are combined by multiplication.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!