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Question 3
3 pts
Solve the following three variable word problem
"Cindy sells beaded necklaces. She has three types, type A, B and C. Cindy has a total of 30
necklaces that she plans on selling. Necklace A she sells for $10 while B and C are sold for
$12 and $15 respectively. If she sells all her necklaces at these prices, she will make $395.
The sum of the number of necklaces for A and B is equivalent to the number of necklaces she
has for C. Find how many necklaces she has of each type?
O
A=10, B=5 and C=15
O
A=8, B=8 and C=14
O
A=5, B=10 and C=15
© A=10, B=10, C=10

Respuesta :

opudodennis

Answer:

A=5, B=10 and C=15

Step-by-step explanation:

-We are given that:

[tex]A+B+C=30\\\\A+B=C\\\\\therefore 2C=30\\\\C=15\\\\A+B=30-15=15\ \ \ \ ...i[/tex]

-Also, given that:

[tex]10A+12B+15C=395, \ C=15\\\\10A+12B=395-15\times 15\\\\10A+12B=170\ \ \ \ \ \ ...ii[/tex]

From equation i, we have that:

[tex]A=15-B[/tex]

#we substitute A=15-B in equation ii to solve for B:

[tex]10A+12B=170\\\\10(15-B)+12B=170\\\\150A-10B+12B=170\\\\2B=20\\\\B=10\\\\\therefore A=15-10=5[/tex]

Hence, the values of our unknowns are A=5, B=10 and C=15