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
Sophie [7]
3 years ago
14

four pencils and a ruler cost $1. six pencils and three rulers cost $2.10. find the cost of three pencils and thirteen rulers.​

Mathematics
1 answer:
deff fn [24]3 years ago
5 0

Answer:

$ 5.65

Step-by-step explanation:

let the cost of a pencil and a ruler be $p and $r respectively.

4p +r= 1 -----(1)

6p +3r= 2.10

divide by 3 throughout:

2p +r= 0.70 -----(2)

Q: 3p +13r= ?

(1) -(2):

(4p +r) -(2p +r)= 1 -0.70

4p +r -2p -r= 0.30 <em>(</em><em>expand</em><em>)</em>

2p= 0.30 <em>(</em><em>simplify</em><em>)</em>

p= 0.30 ÷2 <em>(</em><em>÷</em><em>2</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em><em>)</em>

p= 0.15

subst. into (1):

4(0.15) +r= 1

r +0.60= 1

r= 1 -0.60

r= 0.40

cost of three pencils and thirteen rulers

= 3p + 13r

= 3(0.15) + 13(0.40)

= 0.45 + 5.20

= $5.65

You might be interested in
Using the digits 1 to 9 at most one time each, fill in the boxes to find the largest (or smallest) possible values for x.
Mice21 [21]

Answer:

smallest: 8x -3 = 4; 1y +9 = 2. total = -49/8

 largest: 1x -9 = 8; 2y +3 = 7. total = 19

Step-by-step explanation:

If we use variables to represent the box contents, we can write ...

ax -b = c

dy +e = f

Then the values of x and y are ...

 x = (c +b)/a

 y = (f -e)/d

For positive integer values of the variables, x will always be positive, and y may or may not be negative.

Smallest sum

For the sum to be the smallest, we must have x be as small as possible and the ratio (f-e)/d be as negative as possible.

x will be small for large 'a' and for (c+b) small. For y to be as negative as possible, we want 'd' and 'f' small and 'e' large. Best results are obtained for

8x -3 = 4   ⇒   x = 7/8

1y +9 = 2   ⇒   y = -7

For these coefficients, the sum is -6 1/8 = -49/8.

(note that the values of 'b' and 'c' can be swapped with no net effect)

Largest sum

For the sum to be the largest, we must have x as large as possible: (b+c) large and 'a' small. At the same time we must have y be positive and as large as possible: (f-e) positive and large, 'd' small. Best results are obtained for

1x -9 = 8  ⇒   x = 17

2y +3 = 7   ⇒   y = 2

For these coefficients, the sum is 19. Again, 'b' and 'c' can be swapped with no effect.

_____

Additional comment

These extreme values are verified by examination of the 60,480 possible permutations of the coefficients.

8 0
3 years ago
The selling price of an item is $600. It is marked down by 10%, but this sale price is still marked up
Lena [83]

Step-by-step explanation:

Sale price

= Marked down by 10% from selling price

= 90% of selling price

= 0.9 * $600

= $540.

Sale price - Cost price

= $540 - $450 = $90.

The markup from cost to sale is $90.

6 0
2 years ago
Dune Plant
rodikova [14]

Answer:

what

Step-by-step explanation:

3 0
2 years ago
4a/3-b/4=6<br> 5a/6+b=13<br> Solve linear system by elimination
kondor19780726 [428]
\bf \cfrac{4a}{3}-\cfrac{b}{4}=6&#10;\qquad \qquad &#10;\cfrac{5a}{6}+b=13&#10;\\\\\\&#10;\textit{let us remove the denominators off those folks}\\&#10;\textit{by multiplying the first one by 12, both sides}\\&#10;\textit{and the second one by 6, both sides, thus}&#10;\\\\\\&#10;12\left( \cfrac{4a}{3}-\cfrac{b}{4} \right)=12(6)\implies 16a-4b=72&#10;\\\\\\&#10;6\left( \cfrac{5a}{6}+b \right)=6(13)\implies 5a+6b=78

\bf  \textit{now, let's do the elimination}&#10;\\\\&#10;&#10;\begin{array}{llll}&#10;16a-4b=72&\boxed{\times 3}\implies &48a-\underline{12b}=216\\\\&#10;5a+6b=78&\boxed{\times 2}\implies &10a+\underline{12b}=156\\&#10;&&--------\\&#10;&&58a+0\quad=372&#10;\end{array}

solve for "a", once you get "a", plug it back into either equation to get "b"
3 0
3 years ago
PLEASE ANSWER ASAP! IM IN A RUSH!
rewona [7]
1 is A - just plug and chug
2 is B - for 2 linear equations to have infinite solutions they mustbe the same
3 is C
4 is C - that is where they intersect
5 is A - same slope and different intercepts means no solutions
5 0
3 years ago
Read 2 more answers
Other questions:
  • Given a cube with a volume of 27 cm3, what is the volume of a square pyramid that can fit perfectly inside the cube?
    12·1 answer
  • Of 50 students surveyed, 19 said they had soda for breakfast. write a portion in fraction, decimal, percent
    12·1 answer
  • Can you help me please?
    6·1 answer
  • Circles and angles: find f
    10·1 answer
  • How many are 4 x 4 ?​
    12·1 answer
  • Rewrite the expression with a rational exponent as a radical expression
    7·1 answer
  • Patsy can decorate 3 1/2 cakes in 1/4 hour. At this rate, how many cakes can she decorate in 1 hour?
    6·1 answer
  • 9-x/5=3 solve the folloswing equation for x
    13·2 answers
  • PLEASE HELP!!! DUE IN 10 MIN!!!
    13·1 answer
  • Cecilia bought 24 bottles of juice that each contained 12 fluid ounces of juice. How many pints of juice did she buy?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!