5. A sporting goods store sells right-handed and left-handed baseball gloves. In one month, 12 gloves

were sold for a total of $561. Right-handed gloves cost $45 each and left-handed gloves cost $52

each. How many of each type of glove were sold?

The number of left-handed gloves sold=3

The number of right-handed gloves sold=9

Step-by-step explanation:

The expression for the total cost of the gloves can be expressed as;

Total cost = (Cost per right handed glove*number of right handed gloves sold) + (cost per left handed gloves*number of left handed gloves sold)

where;

Total cost=$561

Cost per right handed glove=$45

number of right handed gloves sold=r

cost per left handed gloves=$52

number of left handed gloves sold=l

replacing;

561 = (45*r) + (52*l)

45 r+52 l=561 ... equation 1

The expression for the total number of the gloves sold can be expressed as;

total number of gloves sold=number of right handed gloves sold+number of left handed gloves sold

where;

total number of gloves sold=12

number of right handed gloves sold=r

number of left handed gloves sold=l

replacing;

r+l=12 ... equation 2

Combine equation 1 and 2 and solve simultaneously;

45 r+52 l=561>>>45 r+52 l=561

-

45 (r+l=12) >>>45 r+45 l=540

(45 r-45 r) + (52 l-45 l) = 561-540

7 l=21

l=21/7=3

l=3

replacing the value of l in equation 2

r+3=12

r=12-3=9

r=9

The number of left-handed gloves sold=3

The number of right-handed gloves sold=9