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3 years ago

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Mathematics

1 answer:

allsm [11]3 years ago

4 0

Answer:

Jennifer has 7 quarters

Step-by-step explanation:

The correct question is

Jennifer has $ 3.51 in change in her piggy bank. The change consists of 51 coins inducing pennies, nickels and quarters. If there are 3 times as many nickels as pennies, how many quarters does she have?

Remember that

$1\ penny=\$0.01\\1\ nickel=\$0.05\\1\ quarter=\$0.25$

Let

x ----> the number of pennies

y ---> the number of nickels

z ---> the number of quarters

we know that

$x+y+z=51$ -----> equation A

$0.01x+0.05y+0.25z=3.51$ ----> equation B

$y=3x$ ---> equation C

substitute equation C in equation A and equation B

$x+3x+z=51$

$4x+z=51$ -----> equation D

$0.01x+0.05(3x)+0.25z=3.51$

$0.16x+0.25z=3.51$ ----> equation E

we have

$4x+z=51$ -----> equation D

$0.16x+0.25z=3.51$ ----> equation E

Solve the system of equations D and E by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (11,7)

x=11,z=7

see the attached figure

Find the value of y

$y=3(11)=33$

The number of pennies is 11

The number of nickels is 33

The number of quarters is 7

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A minor league baseball team plays 128 games a seanson. If the tam won 16 more than three times as many games as they lost how m

tiny-mole [99]

Answer: The team won 100 games and losses 28 games

Step-by-step explanation:

Let the number of games won denoted by x and the games lost is denoted by y .

Given : A minor league baseball team plays 128 games in a season.

Team won 16 more than three times as many games as they lost.

Then, the system of equations, we have

$x+y=128-------(1)\\\\x=3y+16------------(2)$

We can rewrite equation (2) as $x-3y=16----------------(3)$

Now, Eliminate equation (3) from (1), we get

$y-(-3y)=128-16\\\\\Rightarrow\ 4y=112\\\\\Rightarrow\ y=\dfrac{112}{4}=28$

Substitute the value of y in (2), we get

$x=3(28)+16=84+16=100$

Hence, the team won 100 games and losses 28 games.

7 0

3 years ago

There are three consecutive even integers. If twice the first integer added to the second is 268,244, find all three integers.

r-ruslan [8.4K]

Answer:

89414,89416,89418

Step-by-step explanation:

Let n bet the positive integer and then 2n is an even integer because multiplying n with 2 makes it an even integer.

Now, 2n+2, 2n+4 are the next integers.

Therefore, three consecutive integers are: 2n, 2n+2, 2n+4.

It is given that twice the first integer added to the second is 268,244 that means:

$2(2n)+(2n+2)=268244$

$4n+2n+2=268244$

$6n=268242$

$n=44707$

Therefore, three consecutive integers are:

2n=89414, 2n+2=89416, 2n+4=89418

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3 years ago

When the weght of apples is increased by 4 what is the total cost increase

inn [45]

The answer will be is 1

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3 years ago

Carly lives in Scottsdale, AZ and plans to go visit downtown Glendale, AZ. The map with a scale of 2 cm for every 4 km shows the

AleksandrR [38]

Comparing map distance to real distance we get 2cm/4km. That means 1cm = 2km.

So the map distance is half the real distance (well, technically not as one is in cm and the other in km but it’s enough to think this way) and a real distance of 10km must mean a map distance of half that (again ignoring the units) so we get 5cm.

5 0

3 years ago

Read 2 more answers

(x+12) (3x+2) Find the value of X

KatRina [158]

Step-by-step explanation:

Equation at the end of step 1

(3x2 - 38x) + 24 = 0

STEP2:Trying to factor by splitting the middle term

2.1 Factoring 3x2-38x+24

The first term is, 3x2 its coefficient is 3 .

The middle term is, -38x its coefficient is -38 .

The last term, "the constant", is +24

Step-1 : Multiply the coefficient of the first term by the constant 3 • 24 = 72

Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is -38 .

-72 + -1 = -73 -36 + -2 = -38 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -36 and -2

3x2 - 36x - 2x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

3x • (x-12)

Add up the last 2 terms, pulling out common factors :

2 • (x-12)

Step-5 : Add up the four terms of step 4 :

(3x-2) • (x-12)

Which is the desired factorization

Equation at the end of step2:

(x - 12) • (3x - 2) = 0

STEP3:Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

3.2 Solve : x-12 = 0

Add 12 to both sides of the equation :

x = 12

Solving a Single Variable Equation:

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3 years ago

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