Word Problem Question

Question

Jimmy had two wooden sticks of the same length. He cut the first stick into 5 cm pieces and drew 3 yellow dots on each piece. He then cut the second stick into 7 cm pieces and drew 8 pink dots on each piece. Given that there were 190 more pink dots than yellow dots in the end, what was the length of each wooden stick? Please give the answer in centimeters.

Answer 1

Hi Carla,

Your Question: Jimmy had two wooden sticks of the same length. He cut the first stick into 5 cm pieces and drew 3 yellow dots on each piece. He then cut the second stick into 7 cm pieces and drew 8 pink dots on each piece. Given that there were 190 more pink dots than yellow dots in the end, what was the length of each wooden stick? Please give the answer in centimeters.

Given:

1. 2 sticks of the same length
2. Stick 1 cut into 5cm pieces with 3 Yellow dots each
3. Stick 2 cut into 7cm pieces with 8 pink dots each
4. There are 190 more pink dots than yellow dots

Find: The length of the sticks in cm

Let L = the length of each stick. They are the same length

Stick 1: the number of yellow dots (Y) would be equal to the length divided by 5 cm times 3 dots each piece

Y= 3dots (L/5cm)

Stick 2: The number of Pink dots (P) would be the length divided by 7cm times 8 dots each

P=8dots (L/7cm)

There are 190 more pink dots than yellow dots

Pink dots = yellow dots plus 190

P = Y + 190

Now you can use substitution

Y=3(L/5) P=8(L/7) P=Y+190

8L/7 = 3L/5 +190

8L/7 - 3L/5 = 190

(40L-21L)/35 = 190

19L=6650

L = 350 cm

Lets check if this works out, if it does, we should find there are 190 more pink dots than yellow

Y = 3L/5 = 3(350)/5 = 210

P = 8L/7 = 8(350)/7 = 400

400-210=190

So our answer checks out.

Hope this helps!