All categories

2 years ago

Jalen has $10.35 in quarters and nickels he has a total of 99 coins how many of each coins does he have?

Mathematics

1 answer:

melisa1 [442]2 years ago

3 0

Answers:

72 nickels and 27 quarters

========================================

Work Shown:

$10.35 = 1035 cents

q = number of quarters

n = number of nickels

n+q = 99 is the total number of coins. This solves to q = -n+99

25q = value of all the quarters in cents

5n = value of all the nickels in cents

5n+25q = 1035 is the total value in cents

------------------

5n+25q = 1035

5n+25( q ) = 1035

5n+25( -n+99 ) = 1035

5n - 25n + 2475 = 1035

-20n + 2475 = 1035

-20n = 1035-2475

-20n = -1440

n = -1440/(-20)

n = 72

Jalen has 72 nickels

q = -n+99

q = -72+99

q = 27

Jalen has 27 quarters

----------------------

Check:

n+q = 72+27 = 99

5n+25q = 5*72+25*27 = 1035

This confirms the answers.

You might be interested in

Please answer this in two minutes

diamong [38]

Answer:

366.6 mm²

Step-by-step explanation:

Step 1: find XY using the Law of sines.

Thus,

$\frac{XY}{sin(W)} = \frac{WY}{sin(X)}$

m < W = 180 - (70+43) (sum of angles in a triangle)

W = 180 - 113 = 67°

WY = 24 mm

X = 43°

XY = ?

$\frac{XY}{sin(67)} = \frac{24}{sin(43)}$

Cross multiply:

$XY*sin(43) = 24*sin(67)$

$XY*0.68 = 24*0.92$

Divide both sides by 0.68 to solve for XY

$\frac{XY*0.68}{0.68} = \frac{24*0.92}{0.68}$

$XY = 32.47$

XY ≈ 32.5 mm

Step 2: find the area using the formula, ½*XY*WY*sin(Y).

Area = ½*32.5*24*sin(70)

Area = ½*32.5*24*0.94

= 32.5*12*0.94

Area = 366.6 mm² (nearest tenth)

6 0

3 years ago

Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the paraboloid z = 7x2 + y2 and the

Akimi4 [234]

Letting $x=t$ , we get $y=3x^2=3t^2$ and $z=7x^2+y^2=7t^2+(3t^2)^2=7t^2+9t^4$ , so we can parameterize the intersection by

$\mathbf r(t)=\langle t,3t^2,7t^2+9t^4\rangle$

where $-\infty$ .

Image attached.

5 0

3 years ago

PLZZZZZZZZZZZZZZZZZ HELP!

zheka24 [161]

Answer:

-8

Step-by-step explanation:

5(x+12)= 20

5x+60= 20

5x= -40

x= -8

3 0

3 years ago

For how many integers $n$ is it true that $\sqrt{n} \le \sqrt{4n - 6} < \sqrt{2n + 5}$?

ale4655 [162]

$\bf \sqrt{n}\leqslant \sqrt{4n-6}$

$\bf \sqrt{n}< \sqrt{2n+5}\implies \stackrel{\textit{squaring both sides}}{n< 2n+5}\implies 0\leqslant 2n - n + 5 \\\\\\ 0 < n+5\implies \boxed{-5 < n} \\\\\\ \stackrel{-5\leqslant n < 2}{\boxed{-5}\rule[0.35em]{10em}{0.25pt}0\rule[0.35em]{3em}{0.25pt}2}$

namely, -5, -4, -3, -2, -1, 0, 1. Excluding "2" because n < 2.

6 0

3 years ago

How do you use equivalent rates in the real world?

kotykmax [81]

Cross multiplication
or multiplying by a number which goes in both rates

7 0

3 years ago