Solve The Problem?

Question

On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $4 each and a number of necklaces at $13 each. She wrote a check for $1110 to pay for the order. How many bracelets and how many necklaces did Rosaria purchase?

a. 50 bracelets and 70 necklaces
b. 45 bracelets and 75 necklaces
c. 55 bracelets and 65 necklaces
d. 60 bracelets and 60 necklaces

Answer 1

let b = # of bracelets
120-b = # of necklaces

4b + 13(120-b) = 1110
4b + 1560 - 13b = 1110
-9b = -450
b = 50
50 bracelets and 70 necklaces (a)

that's it! :)

Answer 2

Subititution Method

let

b = bracelets

n = Necklaces

120 = total bracedlets and necklaces

4b = cost of bracelets

13b = cost of necklaces

1110 = total cost of bracklets and necklaces
- - - - - - - -

b + n = 120- - - - - - - Equation 1
4b + 13n = 1110- - - Equation 2
- - - - - - - - -

Isolate b in equation 1

b + n = 120

Transpose n

b + n - n = - n + 120

b = - n + 120

Substitute the b value in equation 2
- - - - - - - - -

4b + 13n = 1110

4(- n + 120) + 13n = 1110

- 4n + 480 + 13n = 1110

Collect like terms

9n + 480 = 1110

Transpose 480

9n + 480 - 480 = 1110 - 480

Collect like terms

9n = 630

Divide both sides of the equation by 9

9n / 9 = 630 / 9

n - 630/9

n = 70. . .←. .Number of necklaces

Substitute the n value in equation 1
- - - - - - -

b + n = 120

b + 70 = 120

Transpose 70

b + 70 - 70 = 120 = 70

Collect like terms

b = 50. . .←. .Number of bracelets

Substitute the b value into equation 1

- - - - - - - - - -

Check for equation 1

b + n = 120

50 + 70 = 120

120 = 120
- - - - - - - - -

Check for equation 2

4b + 13n = 1110

4(50) + 13(70) = 1110

200 + 910 = 1110

1110 = 1110
- - - - - - - - - -

Both equations balance

There are 50 bracelaces and 70 necklaces
- - - - - - - - -s-

Answer 3

let no. of bracelets be x.
so no. of necklaces be 120 - x.

according to question

4x + 13(120 - x) = 1110

4x + 1560 - 13x = 1110

-9x = 1110 - 1560

-9x = -450

x = 450/9 both minus sign to be removed.

x =50

so, bracelets = 50

necklaces =120 - 50
= 70
ans. a

Answer 4

[02]
Let her purchase x pieces of bracelets and 120-x pieces of necklaces
By the problem,
4x+13(120-x)=1110
4x+1560-13x=1110
-9x=1110-1560= -450
x= -450/-9=50
Therefore she purchased 50 bracelets and 120-50 or 70 necklaces
Therefore (a) is correct

Answer 5

Answer is A.

(50 * 4) + (70 * 13) = 200 + 910 = 1110.

Answer 6

you know that if:
x=bracelets
y=necklaces

then:
x+y=120
4x+13y=1110

this is a system of equations, and obviously, it's a bit difficult to solve with two variables. that means you need to solve for one variable, and then plug in to find the other.

so, first thing you'll do is to solve for one variable.

x+y=120
x=120-y

plug in to the second equation...
4(120-y)+13y=1110

distribute
480 - 4y +13y=1110

combine like terms
9y = 630

divide to solve for y
y=70

now plug in to find x
4x+13(70)=1110

4x+910=1110

4x=200

x=50

that's 70 necklaces and 50 bracelets.
choice A is your answer.

Answer 7

start
accessories
calculator
50 + 4 (M+)
70 * 13 (M+)
then MR for memory recall to see your total -

if A doesn;t work - try b - c - d
until you get 1100 as an answer - -

dont forget to do MC =memory clear

between problems

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