Jasmine started running in March and kept track of how many miles she ran each month. In April, she ran 7 more miles than in March. In May, she increased the number of miles she ran in April by 50% and ran 78 miles.

Question

We'll use m to represent the number of miles Jasmine ran in March. Choose the tape diagram that represents the distance Jasmine ran in April.

m
March

April
7
m

m
March

April
7
m
Excellent!
Choose the tape diagram that represents the distance Jasmine ran in May.

m
March

April
7
m

May
78

m
March

April
7
m

May
78
You got it!
Write an equation in words to represent this situation.
m
March

April
7
m

May
78

50% of April's distance = May's distance

20% of April's distance = May's distance

120% of April's distance = May's distance

150% of April's distance = May's distance

Write an equation to represent this situation.

Answer 1

To represent the situation with an equation, we start by determining the distance Jasmine ran in April and then find the relationship to her distance in May.

1. Distance in March: Let \( m \) represent the distance Jasmine ran in March.
2. Distance in April: Since she ran 7 more miles than in March, the distance in April can be expressed as: \[ \text{Distance in April} = m + 7 \]
3. Distance in May: Jasmine increased the distance she ran in April by 50% and ran a total of 78 miles. To express this mathematically, we can say: \[ \text{Distance in May} = 1.5 \times \text{Distance in April} \] Substituting the expression for the Distance in April: \[ \text{Distance in May} = 1.5 \times (m + 7) = 78 \]

Putting this all together, we can write the equation in words as: "The distance Jasmine ran in May is equal to 150% of the distance she ran in April."

Final equation: \[ 1.5(m + 7) = 78 \]