Jenny and Mary bought some carrots and tomatoes each. The number
of tomatoes Jenny bought was 60% that of the number of carrots. Mary bought 3/5 as many carrots as tomatoes. Jenny had five times as many carrots and tomatoes as Mary.
(a) What was the ratio of the number of carrots Jenny had to the number of tomatoes Mary bought?
(b) After Mary gave away 14 carrots, the ratio of the number of carrots to the number of tomatoes Mary became 1:4. How many carrots did Mary have in the end?
Organize your information in a chart of two columns, T and C
and two rows, J and M ,
obviously for (T)omatoes, (C)arrots, etc
"The number of tomatoes Jenny bought was 60% that
of the number of carrots"
In the J,C place: x
in the J,T place: 3/5 x , .... 60% is 3/5
"Mary bought 3/5 as many carrots as tomatoes"
in the M,T place : y
in the M,C place: 3/5 y
multiply each entry by 5 to eliminate fractions, (the ratios won't change)
J,C -- 5x
J,T -- 3x
M,T -- 5y
M,C -- 3y
total veggies for J -- 8x
total veggies for M -- 8y
Jenny had 5 times as many veggies as Mary ---> 8x = 5(8y)
or x = 5y
Jenny's carrots : Mary's tomatos = 5x : 5y = x : y
= 5y : y
= 5 : 1
"After Mary gave away 14 carrots, the ratio of the number of carrots to the number of tomatoes Mary became 1:4"
(3y - 14) : 5y = 1 : 4
(3y-14)/5y = 1/4
12y - 56 = 5y
7y = 56
y = 8 , then x = 40
in the original chart:
---- T ---- C
J - 120 200
M - 40 24
at the end Mary had 3y-14 or 10 carrots.
check the data vs the chart, all works out