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
vesna_86 [32]
3 years ago
5

jack bought 4 rulers and 5 compasses for $18.92 altogether. If Jacks brother bought 2 rulers and 4 compasses for $14.98, what wa

s the price of each compass?
Mathematics
1 answer:
love history [14]3 years ago
7 0

Answer:

Price of each compass = $3.68

Price of each ruler = $0.13

Step-by-step explanation:

Let R denote rulers and C denotes compasses

Jack bought 4 rulers and 5 compasses for $18.92

which algebraically translates to

4R + 5C = 18.92   eq. 1

Jack's brother bought 2 rulers and 4 compasses for $14.98

which algebraically translates to

2R + 4C = 14.98   eq. 2

Now we have two equations and two unknowns R and C

Choose any of the above equation and make any of the unknown the subject of the equation.

Choosing eq. 1

4R + 5C = 18.92

4R = 18.92 - 5C

R = (18.92 - 5C)/4    eq. 3

Now put this value of R into eq. 2

2R + 4C = 14.98

2((18.92 - 5C)/4) +4C = 14.98

9.46 - 2.5C + 4C = 14.98

1.5C = 5.52

C = 5.52/1.5

C = 3.68

So the price of each compass is $3.68

We can verify whether our answer is right or not. First we have to find the cost of R

Put this value of C into eq. 3

R = (18.92 - 5C)/4

R = (18.92 - 5*3.68)/4

R = (18.92 - 18.4)/4

R = 0.52/4

R = 0.13

So the price of each ruler is $0.13

Now let us verify:

from eq. 1

4R + 5C = 18.92

4(0.13) + 5(3.68) = 18.92

0.52 + 18.4 = 18.92

18.92 = 18.92  (hence proved)

from eq. 2

2R + 4C = 14.98

2(0.13) + 4(3.68) = 14.98

0.26 + 14.72 = 14.98

14.98 = 14.98  (hence proved)

You might be interested in
There are 3 different roads from city a to city b and 2 different roads from city b to city
Nat2105 [25]

3\cdot2=6

7 0
3 years ago
If a-4=1/a^(x-1) then x=?​
bezimeni [28]
X is got to a specific number but im not sure yet
6 0
2 years ago
Amy mixed together 2.4 gal. of Brand A fruit drink and 5.6 gal. of apple juice. Find the percent of fruit juice in Brand A if th
stellarik [79]

Answer:

D

Step-by-step explanation:

The fruit punch has 2.4 gallons but x %

Apple juice has 5.6 gallons but 100 % or 1

The total mixture would then have 8 gallons and 82 %.

2.4+5.6=8

8×0.82 = 6.56

Then you would do 2.4x + 5.6(1) = 6.56

2.4x + 5.6 = 6.56

2.4x = 0.96

0.96/2.4 = 0.4 = 40%

Therefore, Brand A has 40% fruit juice

5 0
3 years ago
Could somebody please help me with this?
BARSIC [14]

For this problem, we are going to use the Remainder Theorem. This says that for x - n to be a factor of a polynomial p(x), then p(n) = 0. Essentially, it says that x - n is a factor if when you substitute n into the polynomial you get a result of 0.


Thus, in our case, when we substitute x = 2 into the polynomial, we should get an answer of 0 if x - 2 is a factor of the polynomial. Given this information, we can solve for c:

p(2) = 2^3 - 4(2^2) + 2c + 2 = 0

8 - 16 + 2c + 2 = 0

2c - 6 = 0

2c = 6

c = 3


The solution is c = 3.

7 0
3 years ago
Read 2 more answers
Solve the literal equation for y a=9y-3yx
Novay_Z [31]
a=9y-3yx\\\\a=y\big(9-3x\big)\quad|:\big(9-3x\big)\\\\\\\boxed{y=\frac{a}{9-3x}}\qquad \text{for}\quad x\neq 3
6 0
3 years ago
Read 2 more answers
Other questions:
  • Can someone tell me the answer to this question
    14·1 answer
  • Suppose ABCD is a rectangle. Find AB and AD if point M is the midpoint of
    11·1 answer
  • Please see attachment
    7·1 answer
  • Mia is three years older than twice her sister brooke's age. The sum of their ages is less than 30. what is the greatest age Bro
    5·1 answer
  • On an algebra test, there were 3 As, 5 Bs, 10 Cs, 8 Ds, and 4 Fs. What is the probability distribution for the grades A, B, C, D
    14·2 answers
  • The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of 1
    7·1 answer
  • The circle shown has the center o and the measure of angle aob is 45. if the area of the shaded sector is 18 pi what is the radi
    15·1 answer
  • What is(14x2-27x+9)/(7x-3)?
    13·1 answer
  • Create Write a real-world problem that can be<br> solved using the equation 9 + 4x = 21 - 2x
    6·1 answer
  • ⅗ = 6/x<br><br><br> help dont scsm meh
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!