Question

URGENT!!!!!

A local shelter received a generous donation of $2,346 to purchase blankets, sweaters,
and coats. Blankets cost $6 each, sweaters cost $18 each, and coats cost $24 each. The
number of blankets they purchase is seven times the number of coats. The number of
sweaters purchased is twice the number of coats. Write a system of equations that can
be used to determine the number of blankets, , the number of sweaters, , and the
number of coats, , purchased by the shelter.

Answer 1

• Blankets : 161
• Sweaters : 46
• Coats : 23

Task :

• To work out the number of blankets , sweaters and the coats purchased by the shelter

Solution :

Let the number of coats be x , number of Sweaters be y and the number of blankets be z.

ATQ,

• y = 2x....(1)
• z = 7x .....(2)

Moreover,

• $24x + $18y + $6z = $2,346.....(3)

Plugging in the value of y and z from equation (1) & (2) in equation (3),

• $24x + $18(2x) + $6(7x) = $2,346
• $24x + $36x + $42x = $2,346
• $102x = $2,346
• x = $2,346/$102
• x = 23

Thus, the number of coats purchased is 23.

We can further plug in the value of x in eq(1) and eq(2) to find out the number of sweaters and that of the blankets respectively.

• y = 2x = 2*23 = 46
• z = 7x = 7*23 = 161

Thus, the shelter purchased a total of 23 coats, 46 sweaters and 161 blankets for the shelter.

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