Jaime bought a box of sweets. She divided 1/2 of the sweets equally into 5 cans and the other half equally into 6 jars. There were 42 sweets in 1 can and 3 jars altogether. How many sweets did she buy?
Let's start by finding out how many sweets Jaime put in each jar. We know that she divided half of the sweets equally into 6 jars, so each jar had:
1/2 ÷ 6 = 1/12
of the sweets.
We also know that there were 3 jars in total, so Jaime put:
3 × 1/12 = 1/4
of the sweets into the jars.
Now we can find out how many sweets Jaime bought. We know that she divided half of them equally into 5 cans, so each can had:
1/2 ÷ 5 = 1/10
of the sweets.
We also know that there were 42 sweets in 1 can, so the total number of sweets that Jaime bought was:
42 × 5 × 10 = 2100
So Jaime bought 2100 sweets in total.
Let's solve this step-by-step:
Step 1: Let's represent the number of sweets Jaime bought as "x".
Step 2: Jaime divided half of the sweets equally into 5 cans, so she divided x/2 sweets into 5 cans. Therefore, each can will have (x/2) / 5 = (x/2) * (1/5) = x/10 sweets.
Step 3: Jaime also divided the other half equally into 6 jars. So, each jar will have (x/2) / 6 = (x/2) * (1/6) = x/12 sweets.
Step 4: The total number of sweets in 1 can is given as 42 sweets. So, we can represent this as x/10 = 42.
Step 5: To find the value of x, we can solve the equation: (x/10) = 42.
Multiplying both sides of the equation by 10, we get: x = 420.
Therefore, Jaime bought 420 sweets.