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