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2 years ago

If a sweatshirt is on sale for 35% and now costs $52, what was the original price?

2 answers:

8 0

The original price was $70.2. (If it’s not supposed to have cents then it’s just $70).

This is because you convert 35% to 1.35. Then, you multiply 52 by 1.35. That’ll give you 70.2.

CaHeK987 [17]2 years ago

8 0

Answer:

The original price of the sweatshirt is $80.

Step-by-step explanation:

If a product is on sale for a 35% discount, then it is 65% of the original price ( because 100 - 35 = 65)

So set up a proportion,

((part)/(whole)) = ((x)/(100))

In the given information, we know that the part (the amount paid) is 52$, what we need to find is the whole. To make solving the problem easier, let's call the whole x.

((52)/(x)) = ((65)/(100))

Simplify,

52/x = 13/20

Cross multiply,

1040 = 13x

Inverse operations,

1040 = 13x

/13 /13

80 = x

So the original price of the sweatshirt is $80.

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1. 5 Burgers and 3 orders of fries cost $34. 4 Burgers and 4 orders of fries cost $32. How much does each burger and each order

Elena L [17]

Answer:

a burger costs $5

an order of fries costs $3

7 pennies

14 nickels

23 dimes

Step-by-step explanation:

x = price of a burger

y = price of a order of fries

5x + 3y = 34

4x + 4y = 32

x + y = 8

x = 8-y

5×(8-y) + 3y = 34

40 - 5y + 3y = 34

-2y = -6

y = $3

x = 8 - 3 = $5

x = number of pennies

y = number of nickels

z = number of dimes

0.01×x + 0.05×y + 0.1×z = 3.07

y = 2x

x + y + z = 44

x + 2x + z = 44

3x + z = 44

z = 44 - 3x

0.01×x + 0.05×2x + 0.1×z = 3.07

0.11×x + 0.1×z = 3.07

0.11×x + 0.1×(44-3x) = 3.07

11x + 10×(44-3x) = 307

11x + 440 - 30x = 307

-19x = -133

x = 7

y = 2×7 = 14

z = 44 - 3×7 = 44 - 21 = 23

7 0

2 years ago

The sum to infinity of a geometric series is 32.The sum of the first four terms is 30 and

gayaneshka [121]

The terms in the series are

$\displaystyle \sum_{n=1}^\infty ar^{n-1} = a + ar + ar^2 + ar^3 + \cdots$

The series converges, so we $|r|$ . All the terms in this particular series are known to be positive, so $0Consider the [tex]N$ -th partial sum of the series,

$S_N = \displaystyle \sum_{n=1}^N ar^{n-1} = a + ar + ar^2 + \cdots + ar^{N-1}$

Multiply both sides by $r$ :

$r S_N = ar + ar^2 + ar^3 + \cdots + ar^N$

Subtracting this from $S_N$ eliminates all the $r^n$ terms between $n=1$ and $n=N-1$ , leaving us with

$(1 - r) S_N = a - ar^N \implies S_N = \dfrac{a(1-r^N)}{1-r}$

As $N\to\infty$ , the $r^N$ term will converge to zero, and the value of the infinite series is

$\displaystyle \sum_{n=1}^\infty ar^{n-1} = \lim_{n\to\infty} S_N = S = \frac a{1-r}$

Now, we're given

$S = \dfrac a{1-r} = 32 ~~~~ \text{ and } ~~~~ S_4 = \dfrac{a(1-r^4)}{1-r} = 30$

By substitution, we have

$S_4 = 32(1-r^4) = 30 \implies 1-r^4 = \dfrac{15}{16} \implies r^4 = \dfrac1{16} \implies r = \dfrac12$

so that

$S = \dfrac a{1 - \frac12} = 32 \implies a = 16$

Then the sum of the first 8 terms is

$S_8 = \dfrac{a(1-r^8)}{1-r} = \dfrac{16\left(1 - \frac1{2^8}\right)}{1-\frac12} = \dfrac{255}8$

and the difference between this and the infinite sum is

$S - S_8 = 32 - \dfrac{255}8 = \dfrac{256-255}8 = \boxed{\dfrac18}$

3 0

1 year ago

At a local sporting goods store, employees get paid a commission that is 6% of their sales. gina's sales for the week was $441.0

Olin [163]

$26.46. To find this answer, you multiply .06 by $441.00 to find the percent. When finding percentages of a total number, you move the decimal place in the percentage over to places to the left and multiply that by the total.

8 0

2 years ago

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What are 10 duties of a police without coping and pasting

valina [46]

The primary duty of a police officer<span> is to protect people and property. This really summarizes the "10 Duties of a Police Officer".</span>

4 0

2 years ago

In the figure, PQ is parallel to RS. The length of RP is 5cm; the length of PT is 30cm; the length of QT is 60cm. What is the le

rjkz [21]

The triangles PTQ and RTS are similar; so the ratios of corresponding sides are equal.

Let us denote the unknown length SQ as x.

We could make the following similarity relation;

$\begin{gathered} \frac{30}{30+5}=\frac{60}{60+x} \\ \end{gathered}$

Cross multiply to obtain;

$\begin{gathered} 30(60+x)=60(35) \\ 1800+30x=2100 \\ \text{collect like terms} \\ 30x=2100-1800 \\ 30x=300 \\ \text{divide both sides by 30} \\ \frac{30x}{30}=\frac{300}{30} \end{gathered}$

Therefore;

$x=10\operatorname{cm}$

Therefore, the answer is option A

3 0

6 months ago

If a sweatshirt is on sale for 35% and now costs $52, what was the original price?​

If a sweatshirt is on sale for 35% and now costs $52, what was the original price?