WRITING LITERAK EXPRESSIONS FOR WORD PROBLEMS ON SAT

Problem 1 :

If one book costs c dollars, what is the cost, in dollars, of m books?

(A) m + c     (B) m/c      (C) c/m      (D) mc      (E) mc/100

Solution :

Cost of one book = $c

For example,

Cost of 2 books = $2c

Cost of m books = $mc

Problem 2 :

Represent the cost, in dollars, of k pounds of apples at c cents per pound.

(A) kc     (B) 100kc     (C) kc/100

(D) 100k + c   (E) (k/100) + c

Solution :

Cost of k pounds of apple = c cents per pound.

Total cost = kc cents.

Converting cents to dollars.

1 dollar = 100 cents

1 cent = 1/100 dollars

kc cents = kc/100 dollars.

Problem 3 :

If p pencils cost c cents, what is the cost of one pencil?

(A) c/p     (B) p/c     (C) pc

(D) p - c   (E) p + c

Solution :

Cost of p pencils = c cents

Cost of 1 pencil = c/p cents

Problem 4 :

Express the number of miles covered by a train in one hour if it covers r miles in h hours.

(A) rh    (B) h/r    (C) r/h (D) r + h (E) r – h

Solution :

Distance covered by train in h hours = r miles

Distance covered in 1 hour = r/h miles.

Problem 5 :

Express the number of minutes in h hours and minutes.

(A) mh    (B) (h/60) + m    (C) 60(h + m)

(D) (h + m)/60    (E) 60h + m

Solution :

h hours and m minutes.

Converting hours to minutes :

1 hour = 60 minutes

h hour = 60h minutes

h hour and m minutes = (60 h + m) minutes.

Problem 6 :

Express the number of seats in the school auditorium if there are r rows with s seats each row and s rows with r seats each.

(A) 2rs    (B) 2r + 2s    (C) rs + 2

(D) 2r + s   (E) r + 2s

Solution :

For example,

2 rows each row will consists of 3 seats.

Total number of seats = 2 x 3 = 6 seats.

In the same way,

r rows with s seats = rs seats

s rows with r seats = sr seats.

Total number of seats = rs + sr

= 2sr seats

Problem 7 :

How many dimes are there in n nickels and q quarter ?

(A) 10nq    (B) (n + q)/10    (C) (1/2)n+(5/2)q

(D) 10n + 10q     (E) 2n + (q/10)

Solution :

Total = n/2 + 5q/2

= (1/2)n + (5/2)q

Problem 8 :

Roger rents a car at a cost of D dollars per day plus c cent per mile. How many dollars must he pay if he uses the car for 5 days  and drives 1000 miles ?

(A) 5D + 1000c    (B) 5D + (c/1000)   (C) 5D + 100c

(D) 5D + 10c     (E) 5D + c

Solution :

Rent per one day = 5 dollars

Rent for 5 days = 5 D

Cost for 1 mile = c cent

1000 miles = 1000 cents

1 dollar = 100 cents

1000 cents = 10 c dollar

Total cost = 5D + 10c

Problem 9 :

The cost of a long-distance telephone call is c cents for the first three minutes and m cents for each additional minute. Represent the price of a call lasting d minutes if d is more than 3.

(A) c + md     (B) c + md – 3m     (C) c + md + 3m

(D) c + 3md      (E) cmd

Solution :

Cost for first 3 minutes = 3c cents

m cent for each additional minute.

Number of minutes last = d

Can be decomposed into 3 and (d - 3)

Total cost = 3c + m(d - 3)

= 3c + md - 3m

Problem 10 :

The sales tax in Morgan country is m%. Represent the total cost of an article priced at $D.

A) D + mD    (B) D + 100mD     (C) D + mD/100

(D) D + m/100 (E) D + 100m

Solution :

Cost of an article = D

tax to be paid = m% of D

Total cost = D + m% of D

= D + mD/100